{"as_of":"2026-08-19T03:21:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:18237636e2f924e5fc87967e9445b487a793a1f6c43257735c2699a5c18798c3","coverage":[{"denominator":41,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":41,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-19T08:12:44.029481Z","state":"measured"},{"denominator":42,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":42,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-18T06:34:40.430872+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-21T10:52:14.961955Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-05-21T10:54:07.986296Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","version":2},"cited_work":{"arxiv_id":"2506.18073","doi":null,"metadata_source":"pith","pith_arxiv_id":"2506.18073","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","venue":"math.CO","work_id":"ab37625f-9463-4ff2-96bf-ea35ce60f579","year":2025},"citing_paper":{"arxiv_id":"2603.13798","last_updated":"2026-08-07T14:19:08Z","snapshot_observed_at":"2026-08-14T23:45:22.914602Z","submitted_at":"2026-03-14T07:08:47Z","title":"Iterated Graph Systems (I): random walks and diffusion limits","version":2},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-05-21T10:52:14.961955Z"},"links":{"cited_paper":"/paper/2506.18073","citing_paper":"/paper/2603.13798"},"observation_digest":"sha256:18ca2f562e0feea3c2808a63cfefafcbdafb679aeef5226ff43198fbcf8565c7","observation_id":"84a94a0b-fb85-4dc5-8e19-cad26d847db7","resolution":{"observed_at":"2026-05-21T10:54:07.988026Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2506.18073/citation-record","integrity":"/paper/2506.18073/integrity","json":"/paper/2506.18073/citation-record.json","paper":"/paper/2506.18073"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"On the scale-freeness of random colored substitution networks","venue":null,"work_id":"d2de562d-ee15-4896-a191-1badaa55db91","year":2024},"citing_paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-05-19T08:12:44.029481Z"},"links":{"citing_paper":"/paper/2506.18073"},"observation_digest":"sha256:966a5dc5ca8eef0d5073fd0470d555969a9e6b7acc7718974305c0148db84f2e","observation_id":"73dd2f7d-e7f3-40a1-b7f7-9fe98d643bc4","resolution":{"observed_at":"2026-05-19T08:13:02.092725Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Fractal dimensions for iterated graph systems","venue":null,"work_id":"72c35ef1-4600-4569-be7a-2ade0ac76af5","year":2024},"citing_paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-05-19T08:12:44.029481Z"},"links":{"citing_paper":"/paper/2506.18073"},"observation_digest":"sha256:088709d6fb58e428c2de4ce9f73291ef963d6db2dd293795dd758c7672882f5f","observation_id":"7d4531bd-4200-4521-9022-ca6ac3c580e2","resolution":{"observed_at":"2026-05-19T08:13:02.116957Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Recursion equations in gauge field theories","venue":null,"work_id":"3e54f55f-e9f6-441b-a2ea-5f8bf6aa7dc5","year":1996},"citing_paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-05-19T08:12:44.029481Z"},"links":{"citing_paper":"/paper/2506.18073"},"observation_digest":"sha256:764ce61a3ec333c1096b96e9c13a1b4e92d8f38396d349e1b69edbedb128e1da","observation_id":"d57735c7-9ac7-4bde-ae51-9f6311fc2ccb","resolution":{"observed_at":"2026-05-19T08:13:02.120401Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Notes on migdal’s recursion formulas","venue":null,"work_id":"c0a6c984-43a7-4dfa-a16a-be8d02e57b01","year":1976},"citing_paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-05-19T08:12:44.029481Z"},"links":{"citing_paper":"/paper/2506.18073"},"observation_digest":"sha256:be449f759f162ea5f47012251e2012be9777e595f36e1699f9ec2adea6fcfb01","observation_id":"0c19dc67-540e-4d69-990c-6bb1ce8601b3","resolution":{"observed_at":"2026-05-19T08:13:02.128998Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Cluster shapes at the percolation threshold: and effective cluster dimensionality and its connection with critical-point exponents","venue":null,"work_id":"4ff98792-0d80-4847-8fc2-a10d4d566111","year":1977},"citing_paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-05-19T08:12:44.029481Z"},"links":{"citing_paper":"/paper/2506.18073"},"observation_digest":"sha256:74275cfa1daaf1f49e2781e2c200f7ea2713896eae9bbf764fcb366606cf64ff","observation_id":"014d83a9-f3ea-4bd3-809f-91c5769b1d26","resolution":{"observed_at":"2026-05-19T08:13:02.061234Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Renormalisation-group calculations of finite systems: order parameter and specific heat for epitaxial ordering","venue":null,"work_id":"fa30c4b8-f23b-477b-bf15-e485d93f0c73","year":1979},"citing_paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-05-19T08:12:44.029481Z"},"links":{"citing_paper":"/paper/2506.18073"},"observation_digest":"sha256:e968024f63cbc6ca88a4987a59f8727d24aa330c6501492bf9959a5e2056ca77","observation_id":"849af381-199c-4219-9798-9a8affc8e278","resolution":{"observed_at":"2026-05-19T08:13:02.148167Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Exactly soluble ising models on hierar- chical lattices","venue":null,"work_id":"89e593bf-509f-4a3a-a11a-17786ec39313","year":1981},"citing_paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-05-19T08:12:44.029481Z"},"links":{"citing_paper":"/paper/2506.18073"},"observation_digest":"sha256:83b053835ec077b6431dc940e7731593da78e408391c10fcf1c62e9f8f027895","observation_id":"57fc3f02-9998-4b7f-9842-504dc2de206e","resolution":{"observed_at":"2026-05-19T08:13:02.140284Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Density of states on fractals: fractons","venue":null,"work_id":"e1013b1d-bde7-4c8e-bce5-3c8d9b01ff93","year":1982},"citing_paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-05-19T08:12:44.029481Z"},"links":{"citing_paper":"/paper/2506.18073"},"observation_digest":"sha256:ec5c3a52e91df2d796088e5c025991dfe5ff5ceccb4b22dc9490235af1a2ed1d","observation_id":"d9377ea8-aae1-46da-a550-c52c5d881a03","resolution":{"observed_at":"2026-05-19T08:13:02.136642Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Phase transitions on fractals. ii. sierpinski gaskets","venue":null,"work_id":"7ec7b9fe-b851-4d25-84cb-067b3eaba035","year":1984},"citing_paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-05-19T08:12:44.029481Z"},"links":{"citing_paper":"/paper/2506.18073"},"observation_digest":"sha256:faf0af9d899e263c88b3b25c3b5768ad689c98bfab7aee973c9f42e538e3ff6f","observation_id":"6b4b4097-556a-4157-ac76-34688d1041b4","resolution":{"observed_at":"2026-05-19T08:13:02.052352Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Particle-antiparticle annihilation in diffusive motion","venue":null,"work_id":"febd29fd-69d8-402e-a8c2-596dd5d490e6","year":1983},"citing_paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-05-19T08:12:44.029481Z"},"links":{"citing_paper":"/paper/2506.18073"},"observation_digest":"sha256:1d5169418f15fe48f6f1c182549a426b7efdc08a902cea19f6cd4e66bf656aa4","observation_id":"f03785d5-f4b7-44bd-b484-797485d9b9b9","resolution":{"observed_at":"2026-05-19T08:13:02.168452Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Flow in porous media: The","venue":null,"work_id":"500dc487-ca05-4bff-b162-da74c05f6c1f","year":1984},"citing_paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-05-19T08:12:44.029481Z"},"links":{"citing_paper":"/paper/2506.18073"},"observation_digest":"sha256:50f6ffe2149c86c876c88fc8112f0296c4773d680b876ca5fb7bdcb538062ca6","observation_id":"49f0a89f-a313-4659-bc59-a8f6d344259f","resolution":{"observed_at":"2026-05-19T08:13:02.087576Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Fractal structure of zeros in hierarchical models","venue":null,"work_id":"ebc85132-9939-44ba-8c3d-f3e3176d165b","year":1983},"citing_paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-05-19T08:12:44.029481Z"},"links":{"citing_paper":"/paper/2506.18073"},"observation_digest":"sha256:97946c83502755e9a2c81b4d6f6e653304409fa71c21abd11f31d28a6b84ab4e","observation_id":"65fb8b1a-acc9-4e9f-950f-6af537a411f7","resolution":{"observed_at":"2026-05-19T08:13:02.157750Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Self-similarity of complex networks","venue":null,"work_id":"0dd31979-a223-45f7-9d49-bea7361509a5","year":2005},"citing_paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-05-19T08:12:44.029481Z"},"links":{"citing_paper":"/paper/2506.18073"},"observation_digest":"sha256:6bc89e0b579bf0f49b65b18670bb7f25bcb7b05b22a16f04f073beeb1558f849","observation_id":"15fdf7c0-6864-483c-a84e-3fb0b856f95e","resolution":{"observed_at":"2026-05-19T08:13:02.047616Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Collective dynamics of ‘small- world’networks","venue":null,"work_id":"3aa8ac17-8d2b-4b2d-8a92-9efb74c01d1c","year":1998},"citing_paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-05-19T08:12:44.029481Z"},"links":{"citing_paper":"/paper/2506.18073"},"observation_digest":"sha256:b17cefcff0c409f7a52969c70e941c0cfda10e64b07515d5549054b5ef059c50","observation_id":"36dcb52e-aefa-40ab-b689-435f4821c2ac","resolution":{"observed_at":"2026-05-19T08:13:02.164837Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Emergence of scaling in random networks","venue":null,"work_id":"503d4c39-407c-46bf-a810-e31d4a20c754","year":1999},"citing_paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-05-19T08:12:44.029481Z"},"links":{"citing_paper":"/paper/2506.18073"},"observation_digest":"sha256:cc21d257e0da94e4af42dbb811b8525ce50c57426718509d0c49d7e744520c8e","observation_id":"f34ff879-90ec-46d9-9e69-5644b84b104c","resolution":{"observed_at":"2026-05-19T08:13:02.172520Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Hierarchical organization in complex net- works","venue":null,"work_id":"bb9174b2-da05-421c-9819-9c707ab4f3b3","year":2003},"citing_paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-05-19T08:12:44.029481Z"},"links":{"citing_paper":"/paper/2506.18073"},"observation_digest":"sha256:ac7ece2ab1f4fd1831276b5a88ccd444c72293590154442f8ad530376e1fa835","observation_id":"cd50547f-7084-408e-883c-1e27b3f3522c","resolution":{"observed_at":"2026-05-19T08:13:02.097067Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Epidemic spreading in scale-free networks","venue":null,"work_id":"ba771b22-0ebf-4442-93ba-39fc712ac7c5","year":2001},"citing_paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-05-19T08:12:44.029481Z"},"links":{"citing_paper":"/paper/2506.18073"},"observation_digest":"sha256:783ad48eabd2b3379b38af7e435ef45bec4561d8965252c01bf41c10da4ed41f","observation_id":"274dee77-69b6-445f-9d60-5a52b01eafc2","resolution":{"observed_at":"2026-05-19T08:13:02.043194Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Brownian motion on the sierpinski gas- ket","venue":null,"work_id":"a05673f8-6005-4b8d-b569-254d63bb0911","year":1988},"citing_paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-05-19T08:12:44.029481Z"},"links":{"citing_paper":"/paper/2506.18073"},"observation_digest":"sha256:f6d21e62870ce7f1336963780d9f6d9063de5f27f827e662c4284de6b980a52d","observation_id":"605bcbda-6102-4569-b9c7-e0f0b8c16b7a","resolution":{"observed_at":"2026-05-19T08:13:02.056961Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Transition density estimates for brow- nian motion on scale irregular sierpinski gaskets","venue":null,"work_id":"56a67eb9-dd88-4d59-bd93-3c658d3e0a9b","year":1997},"citing_paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-05-19T08:12:44.029481Z"},"links":{"citing_paper":"/paper/2506.18073"},"observation_digest":"sha256:8a47ac284bb01f9b69b74543bf9d7a508ed065a75bf9013ed34b271b0f24f843","observation_id":"8bef0228-d5f5-4cea-8f1a-65cda7da9312","resolution":{"observed_at":"2026-05-19T08:13:02.112656Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Brownian motion and harmonic analysis on sierpinski carpets","venue":null,"work_id":"080bc9f0-7a51-45c6-ae0e-17f4bd61c941","year":1999},"citing_paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-05-19T08:12:44.029481Z"},"links":{"citing_paper":"/paper/2506.18073"},"observation_digest":"sha256:2d751b7a00f3e8faca823dbb1ea52b840ca235a539056114a035e03cce5593b0","observation_id":"87bcf8ae-9ac9-4fb9-9e08-2775f51e037a","resolution":{"observed_at":"2026-05-19T08:13:02.022516Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"A harmonic calculus on the sierpinski spaces","venue":null,"work_id":"854d100e-2159-4427-8295-96515e5321e1","year":1989},"citing_paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-05-19T08:12:44.029481Z"},"links":{"citing_paper":"/paper/2506.18073"},"observation_digest":"sha256:7466da44caf9d2276412a05c1cc9387953584b0311e77c7550964dcd778871d8","observation_id":"28e64162-3cc9-4c72-b9ab-142361ea2760","resolution":{"observed_at":"2026-05-19T08:13:02.038672Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Harmonic calculus on pcf self-similar sets","venue":null,"work_id":"b1747ef4-c2d4-4905-a04c-d59a29417332","year":1993},"citing_paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-05-19T08:12:44.029481Z"},"links":{"citing_paper":"/paper/2506.18073"},"observation_digest":"sha256:554bf471be4b2333b8610de7e04a7de2157f8b22d68706e6106fc6a7b2f47ec4","observation_id":"ee0fb2c2-4cd8-499f-b55b-c0f833384c6c","resolution":{"observed_at":"2026-05-19T08:13:02.034143Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Kigami, Analysis on Fractals","venue":null,"work_id":"2c349135-4cd2-4510-80c2-16deefe818f1","year":2001},"citing_paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-05-19T08:12:44.029481Z"},"links":{"citing_paper":"/paper/2506.18073"},"observation_digest":"sha256:1125251446d478dd581bbd9958d00e4e305ac89491b008ebc79df8052259f51d","observation_id":"7bb066f4-a1f7-40ea-9023-eae5a6229c55","resolution":{"observed_at":"2026-05-19T08:13:02.080445Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Diffusion on the scaling limit of the critical percolation cluster in the diamond hierarchical lattice","venue":null,"work_id":"f365e40f-a667-4771-b268-36fc5cbb9b6f","year":2010},"citing_paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-05-19T08:12:44.029481Z"},"links":{"citing_paper":"/paper/2506.18073"},"observation_digest":"sha256:9fe7623416e10f3f18725ce54c83ad4e279bb07788aa8fe90930d6f475df746b","observation_id":"6c1e5f3b-8356-4f2d-90b5-308f81685540","resolution":{"observed_at":"2026-05-19T08:13:02.105644Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Asymptotics for functions associated with heat flow on the sierpinski carpet","venue":null,"work_id":"b72d9115-02b3-4e40-91eb-14628330eb42","year":2011},"citing_paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-05-19T08:12:44.029481Z"},"links":{"citing_paper":"/paper/2506.18073"},"observation_digest":"sha256:9c7404c4898e2c908717a653b4fecd2049caf087562dc06716ddaf096c99da5e","observation_id":"410afe26-c722-44dd-a861-dabb27a4570a","resolution":{"observed_at":"2026-05-19T08:13:02.152848Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"On the dichotomy in the heat kernel two sided estimates","venue":null,"work_id":"522f57db-9010-4bbc-805c-e929185ec706","year":2008},"citing_paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-05-19T08:12:44.029481Z"},"links":{"citing_paper":"/paper/2506.18073"},"observation_digest":"sha256:66816739b95fa4d5b813313f4b2d9ac56bfae0a8a0236b2bcf7f34f226a260a2","observation_id":"beaac7b6-6ed6-42cb-ba41-de4a61ad2f9f","resolution":{"observed_at":"2026-05-19T08:13:02.028263Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Heat kernels on metric measure spaces and an application to semilinear elliptic equations","venue":null,"work_id":"e0074830-385e-4a3b-98c2-c20824412202","year":2065},"citing_paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-05-19T08:12:44.029481Z"},"links":{"citing_paper":"/paper/2506.18073"},"observation_digest":"sha256:b8daa7edac950e8c02bfc057ff466eaa388adde6409d12f6185fec16208f1d85","observation_id":"dea42b45-3906-41f7-b5a2-2c2e5d4a3468","resolution":{"observed_at":"2026-05-19T08:13:02.109367Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Self-similar k-graph c*-algebras","venue":null,"work_id":"a96ac343-ef64-4be3-9914-49f75996e20f","year":2021},"citing_paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-05-19T08:12:44.029481Z"},"links":{"citing_paper":"/paper/2506.18073"},"observation_digest":"sha256:73f73a509c59b172c2403b4e5095b07c66f3292c47f87c1050a8f938b7de9afe","observation_id":"44e9af7f-a143-49a3-9a82-8f0e18f3adf5","resolution":{"observed_at":"2026-05-19T08:13:02.144384Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Gradient estimate for the heat kernel on some fractal-like cable systems and quasi-riesz transforms","venue":null,"work_id":"01d8a9c5-7c7c-41f2-818b-ac1f0954e043","year":2023},"citing_paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-05-19T08:12:44.029481Z"},"links":{"citing_paper":"/paper/2506.18073"},"observation_digest":"sha256:5dc4728be51f96423e6fb6d613c36501679f4d05abf827b598f517784471c9bc","observation_id":"4215592c-65c1-4d44-b380-60054ca65483","resolution":{"observed_at":"2026-05-19T08:13:02.101231Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Fractality and scale-free effect of a class of self-similar networks","venue":null,"work_id":"c17c6e04-5f5f-44c5-8916-70d70c2fcc4e","year":2017},"citing_paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-05-19T08:12:44.029481Z"},"links":{"citing_paper":"/paper/2506.18073"},"observation_digest":"sha256:74c6f3bfac20a29c400bf9a9006128ba7b81263c42fbdb72a56aca3149e7bc3c","observation_id":"425cc721-ecbe-4062-8fc0-e88d36ac1c24","resolution":{"observed_at":"2026-05-19T08:13:02.123782Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Average distance of substitution networks","venue":null,"work_id":"cae39a20-c142-4668-835d-81f7a13ed1bd","year":2019},"citing_paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-05-19T08:12:44.029481Z"},"links":{"citing_paper":"/paper/2506.18073"},"observation_digest":"sha256:5bd213df266ee4e487729ef100ba1c9d9676e838114ab7ef2de7df237aa34eb3","observation_id":"e91bf039-e095-462e-a5a2-43ea0411ed46","resolution":{"observed_at":"2026-05-19T08:13:02.064762Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Scale-free effect of substitution networks","venue":null,"work_id":"a71ab4ba-99ab-4a43-9835-27ddc6acb386","year":2018},"citing_paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-05-19T08:12:44.029481Z"},"links":{"citing_paper":"/paper/2506.18073"},"observation_digest":"sha256:7e87b1b93142bec1f7bc1e3c4c95cc749c3d9fd790e215b96e455ff98f5af966","observation_id":"0517f5c3-8183-4408-b35c-cbc366fce0aa","resolution":{"observed_at":"2026-05-19T08:13:02.077140Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2406.08062","last_updated":"2024-10-08T11:50:46Z","snapshot_observed_at":"2026-08-16T13:43:49.644212Z","submitted_at":"2024-06-12T10:24:47Z","title":"On Constructions of Fractal Spaces Using Replacement and the Combinatorial Loewner Property","version":2},"cited_work":{"arxiv_id":"2406.08062","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2406.08062","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"On constructions of fractal spaces us- ing replacement and the combinatorial loewner property","venue":null,"work_id":"5d4d1887-9919-4655-b8b8-27bbf9cbc71d","year":2024},"citing_paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-05-19T08:12:44.029481Z"},"links":{"cited_paper":"/paper/2406.08062","citing_paper":"/paper/2506.18073"},"observation_digest":"sha256:5491e5c9fc18fe04677c3d3f93cf0adae9ec5edbc503f1cfc95b342263a9d1e0","observation_id":"055b665c-9d5f-4bb9-aa4d-b8071ab60f7d","resolution":{"observed_at":"2026-05-19T08:13:01.523671Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2408.15692","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Iterated graph systems and the combi- natorial loewner property","venue":null,"work_id":"bcfad66f-8fdb-4e7b-8aeb-c86994f0b5a8","year":2025},"citing_paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-05-19T08:12:44.029481Z"},"links":{"citing_paper":"/paper/2506.18073"},"observation_digest":"sha256:c95c2a5c76228da9e7be6d4df56c2b86dfd3683dc9fef8ba781b11f3129315c9","observation_id":"7d76cdb3-5522-47a3-a99c-3d0489bc8797","resolution":{"observed_at":"2026-05-19T08:13:01.510445Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2505.11356","last_updated":"2026-05-12T15:36:19Z","snapshot_observed_at":"2026-07-06T21:25:08.411184Z","submitted_at":"2025-05-16T15:19:10Z","title":"Fractal Graph Contrastive Learning","version":4},"cited_work":{"arxiv_id":"2505.11356","doi":null,"metadata_source":"pith","pith_arxiv_id":"2505.11356","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Fractal Graph Contrastive Learning","venue":"cs.LG","work_id":"4e195f11-0fa5-4b28-b56c-ed81a67ef9ed","year":2025},"citing_paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-05-19T08:12:44.029481Z"},"links":{"cited_paper":"/paper/2505.11356","citing_paper":"/paper/2506.18073"},"observation_digest":"sha256:cfd5dac0711d3b5cead10d2a7545d93b7d5cad62c03f131c0308fe8ff5324ca9","observation_id":"d52dc4af-3020-48b1-adfa-a0e0a8467369","resolution":{"observed_at":"2026-05-19T08:13:01.503753Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2202.09436","last_updated":"2022-02-18T21:40:47Z","snapshot_observed_at":"2026-08-16T17:20:12.841636Z","submitted_at":"2022-02-18T21:40:47Z","title":"Renormalization Group Approach to Percolation in Hierarchical Lattices","version":1},"cited_work":{"arxiv_id":"2202.09436","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2202.09436","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Renormalization group approach to percolation in hierarchical lattices","venue":null,"work_id":"9ba1f1db-8001-4e03-8fb9-9593f6cda5cd","year":2022},"citing_paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-05-19T08:12:44.029481Z"},"links":{"cited_paper":"/paper/2202.09436","citing_paper":"/paper/2506.18073"},"observation_digest":"sha256:8d5992034866a09b2895f68a1a91ca15cda1203b2edbacc878dc18ae63a9bb0b","observation_id":"6d2ffff2-4466-4b17-a084-8c8050dc0464","resolution":{"observed_at":"2026-05-19T08:13:01.516051Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Percolation on fractal networks: A survey","venue":null,"work_id":"30806107-26d8-4d97-9923-c36ad4547bd9","year":2023},"citing_paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-05-19T08:12:44.029481Z"},"links":{"citing_paper":"/paper/2506.18073"},"observation_digest":"sha256:793a38dfae9c314e6edc73ace66de287a8ce9b7634d9d0d9b69768d7c397e9a8","observation_id":"e1dddb4f-729c-4680-af39-d4b3cb618448","resolution":{"observed_at":"2026-05-19T08:13:02.133453Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Perron-frobenius theory and frequency con- vergence for reducible substitutions","venue":null,"work_id":"62b8693e-9aea-47f7-834e-cd85db6d3f36","year":2016},"citing_paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-05-19T08:12:44.029481Z"},"links":{"citing_paper":"/paper/2506.18073"},"observation_digest":"sha256:be3846f58a72553830cdd6c4589c7699bb75624bc6bd674a692dc0b183b2395e","observation_id":"0601416b-9738-4348-a651-7cea1cec425f","resolution":{"observed_at":"2026-05-19T08:13:02.083925Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Unzerlegbare, nicht negative matrizen","venue":null,"work_id":"e80f4a64-6087-4944-a5c8-fdf3b7d0c524","year":1950},"citing_paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","version":2},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-05-19T08:12:44.029481Z"},"links":{"citing_paper":"/paper/2506.18073"},"observation_digest":"sha256:f100d7b2c216dd01269d3146eebcb91b215785a6f99dc6a8d36a41105af77d75","observation_id":"acb94d94-857c-4caa-8912-ff2dc85820ac","resolution":{"observed_at":"2026-05-19T08:13:02.073017Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"c39d4912-ecdf-4202-9b56-a2e116291069","year":2020},"citing_paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-05-19T08:12:44.029481Z"},"links":{"citing_paper":"/paper/2506.18073"},"observation_digest":"sha256:8bf9c750312a484b23832711c29dc946b0b067a4c0a76a7af63f4e50ceffa558","observation_id":"2c3a69de-fdf8-461a-8030-73e22c6c97ca","resolution":{"observed_at":"2026-05-19T08:13:02.069339Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Falconer, Fractal Geometry: Mathematical Foundations and Applica- tions","venue":null,"work_id":"e0b1a78f-3ef6-4a4d-83bb-fb406fb47052","year":2013},"citing_paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals","version":2},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-05-19T08:12:44.029481Z"},"links":{"citing_paper":"/paper/2506.18073"},"observation_digest":"sha256:1f9db52753c3243fc88c84fcf4a67269632a869136dfdc25b42b3e1dac79e6b6","observation_id":"d4c46c77-e376-4dd9-bf50-76b593b60bfa","resolution":{"observed_at":"2026-05-19T08:13:02.161366Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2506.18073","last_updated":"2026-05-12T13:11:54Z","latest_version":2,"primary_category":"math.CO","snapshot_observed_at":"2026-07-06T21:45:57.248156Z","submitted_at":"2025-06-22T15:40:46Z","title":"Reducible Iterated Graph Systems: multiscale-freeness and multifractals"},"reference_resolution":{"displayed":41,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":1,"verified_exact":4,"verified_fuzzy":36},"total_outbound_references":41},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"thesis":"As of 19 August 2026, this Paper Citation Record lists 41 of 41 outbound references and 1 inbound Pith citation observation for arXiv:2506.18073."}