{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:HTNFHNSBEA2MHSUKY5GPWD37LD","short_pith_number":"pith:HTNFHNSB","canonical_record":{"source":{"id":"1307.2841","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-07-10T16:14:47Z","cross_cats_sorted":[],"title_canon_sha256":"5a4cf54547b3fe8690582b1cfa88e76bfadb535284d3883437b53f3e4684c435","abstract_canon_sha256":"259648c94361fc976874f0aaee89970547b4aafbbd55949720f3e66be16770ed"},"schema_version":"1.0"},"canonical_sha256":"3cda53b6412034c3ca8ac74cfb0f7f58d6df085beeaee43e5ee7b8f2b2f2a896","source":{"kind":"arxiv","id":"1307.2841","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.2841","created_at":"2026-05-18T01:14:59Z"},{"alias_kind":"arxiv_version","alias_value":"1307.2841v4","created_at":"2026-05-18T01:14:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.2841","created_at":"2026-05-18T01:14:59Z"},{"alias_kind":"pith_short_12","alias_value":"HTNFHNSBEA2M","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HTNFHNSBEA2MHSUK","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HTNFHNSB","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:HTNFHNSBEA2MHSUKY5GPWD37LD","target":"record","payload":{"canonical_record":{"source":{"id":"1307.2841","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-07-10T16:14:47Z","cross_cats_sorted":[],"title_canon_sha256":"5a4cf54547b3fe8690582b1cfa88e76bfadb535284d3883437b53f3e4684c435","abstract_canon_sha256":"259648c94361fc976874f0aaee89970547b4aafbbd55949720f3e66be16770ed"},"schema_version":"1.0"},"canonical_sha256":"3cda53b6412034c3ca8ac74cfb0f7f58d6df085beeaee43e5ee7b8f2b2f2a896","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:59.104272Z","signature_b64":"ZZ+rjO+l2Wr9sa52hwsViaD2TeQZqZxkJ35meuDG+WLFspWj8T2CafQdulWNrDQE81C/GdFNP7sgob3dSsb1CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3cda53b6412034c3ca8ac74cfb0f7f58d6df085beeaee43e5ee7b8f2b2f2a896","last_reissued_at":"2026-05-18T01:14:59.103668Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:59.103668Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.2841","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:14:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/IHLNOaAikTE8o//OdnwPJLdNjBCqyBYRSd7V7UZtbmNMR054va4t73AxsgleJm40Qc4cvzycxRnrS/uIaLTDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T20:57:01.281779Z"},"content_sha256":"3112cd6a6a17897f468c2707d3aa78b01b059b6b2c1c6c5aedd44cbf2c93c7b7","schema_version":"1.0","event_id":"sha256:3112cd6a6a17897f468c2707d3aa78b01b059b6b2c1c6c5aedd44cbf2c93c7b7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:HTNFHNSBEA2MHSUKY5GPWD37LD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Projections of self-similar sets with no separation condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"\\'Abel Farkas","submitted_at":"2013-07-10T16:14:47Z","abstract_excerpt":"We investigate how the Hausdorff dimension and measure of a self-similar set $K\\subseteq\\mathbb{R}^{d}$ behave under linear images. This depends on the nature of the group $\\mathcal{T}$ generated by the orthogonal parts of the defining maps of $K$. We show that if $\\mathcal{T}$ is finite then every linear image of $K$ is a graph directed attractor and there exists at least one projection of $K$ such that the dimension drops under the image of the projection. In general, with no restrictions on $\\mathcal{T}$ we establish that $\\mathcal{H}^{t}(L\\circ O(K))=\\mathcal{H}^{t}(L(K))$ for every elemen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2841","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:14:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zu4OqUFJstGownqveNhjI8VSEsroVJbTxGOLrPyFHVnYf0/VsQWBSblZOfZ+J5ETqrK2v8mpjfHfdtkkDOC0Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T20:57:01.282128Z"},"content_sha256":"a8336712ff8cff3ef479c44b413916f1ed6591db8a2c90cab480852d205ff3b3","schema_version":"1.0","event_id":"sha256:a8336712ff8cff3ef479c44b413916f1ed6591db8a2c90cab480852d205ff3b3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HTNFHNSBEA2MHSUKY5GPWD37LD/bundle.json","state_url":"https://pith.science/pith/HTNFHNSBEA2MHSUKY5GPWD37LD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HTNFHNSBEA2MHSUKY5GPWD37LD/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-22T20:57:01Z","links":{"resolver":"https://pith.science/pith/HTNFHNSBEA2MHSUKY5GPWD37LD","bundle":"https://pith.science/pith/HTNFHNSBEA2MHSUKY5GPWD37LD/bundle.json","state":"https://pith.science/pith/HTNFHNSBEA2MHSUKY5GPWD37LD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HTNFHNSBEA2MHSUKY5GPWD37LD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HTNFHNSBEA2MHSUKY5GPWD37LD","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"259648c94361fc976874f0aaee89970547b4aafbbd55949720f3e66be16770ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-07-10T16:14:47Z","title_canon_sha256":"5a4cf54547b3fe8690582b1cfa88e76bfadb535284d3883437b53f3e4684c435"},"schema_version":"1.0","source":{"id":"1307.2841","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.2841","created_at":"2026-05-18T01:14:59Z"},{"alias_kind":"arxiv_version","alias_value":"1307.2841v4","created_at":"2026-05-18T01:14:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.2841","created_at":"2026-05-18T01:14:59Z"},{"alias_kind":"pith_short_12","alias_value":"HTNFHNSBEA2M","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HTNFHNSBEA2MHSUK","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HTNFHNSB","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:a8336712ff8cff3ef479c44b413916f1ed6591db8a2c90cab480852d205ff3b3","target":"graph","created_at":"2026-05-18T01:14:59Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We investigate how the Hausdorff dimension and measure of a self-similar set $K\\subseteq\\mathbb{R}^{d}$ behave under linear images. This depends on the nature of the group $\\mathcal{T}$ generated by the orthogonal parts of the defining maps of $K$. We show that if $\\mathcal{T}$ is finite then every linear image of $K$ is a graph directed attractor and there exists at least one projection of $K$ such that the dimension drops under the image of the projection. In general, with no restrictions on $\\mathcal{T}$ we establish that $\\mathcal{H}^{t}(L\\circ O(K))=\\mathcal{H}^{t}(L(K))$ for every elemen","authors_text":"\\'Abel Farkas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-07-10T16:14:47Z","title":"Projections of self-similar sets with no separation condition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2841","kind":"arxiv","version":4},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3112cd6a6a17897f468c2707d3aa78b01b059b6b2c1c6c5aedd44cbf2c93c7b7","target":"record","created_at":"2026-05-18T01:14:59Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"259648c94361fc976874f0aaee89970547b4aafbbd55949720f3e66be16770ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-07-10T16:14:47Z","title_canon_sha256":"5a4cf54547b3fe8690582b1cfa88e76bfadb535284d3883437b53f3e4684c435"},"schema_version":"1.0","source":{"id":"1307.2841","kind":"arxiv","version":4}},"canonical_sha256":"3cda53b6412034c3ca8ac74cfb0f7f58d6df085beeaee43e5ee7b8f2b2f2a896","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3cda53b6412034c3ca8ac74cfb0f7f58d6df085beeaee43e5ee7b8f2b2f2a896","first_computed_at":"2026-05-18T01:14:59.103668Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:59.103668Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZZ+rjO+l2Wr9sa52hwsViaD2TeQZqZxkJ35meuDG+WLFspWj8T2CafQdulWNrDQE81C/GdFNP7sgob3dSsb1CA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:59.104272Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.2841","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3112cd6a6a17897f468c2707d3aa78b01b059b6b2c1c6c5aedd44cbf2c93c7b7","sha256:a8336712ff8cff3ef479c44b413916f1ed6591db8a2c90cab480852d205ff3b3"],"state_sha256":"3c7fd9f9bd029bb6197ffd5896eead2bb88fa0037eeb3c5f06ebd97638cab589"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s9xBBypQWST2wsjk/KcqhbIaeiziTObcUWAvApb018hc7h+NEHCiMJLY7K00E9oOqjN2n6K70GMfxMBv+mzFBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T20:57:01.284050Z","bundle_sha256":"f8b5bf1ccad1a47019897915d8feec4570d39a46dc71ef118cddcecf69567d9a"}}