{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7WQTBUL3M6WO7OQRGPNWJVZCTF","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":"a02b478f85cea5a9d2680be95f712d583f8dae7157f7b01619f449f70cf2f383","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-04-02T20:24:20Z","title_canon_sha256":"ad36c759a59de01b8eb39160937ecd26f4d1d7851bb28c05ec4fd6c7ddbd4b08"},"schema_version":"1.0","source":{"id":"1604.00555","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.00555","created_at":"2026-05-18T00:47:43Z"},{"alias_kind":"arxiv_version","alias_value":"1604.00555v4","created_at":"2026-05-18T00:47:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.00555","created_at":"2026-05-18T00:47:43Z"},{"alias_kind":"pith_short_12","alias_value":"7WQTBUL3M6WO","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7WQTBUL3M6WO7OQR","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7WQTBUL3","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:74ac2e306504f90dd51dd669b8eed9dd50787512e8fb3cafc974a68406f24eb0","target":"graph","created_at":"2026-05-18T00:47:43Z","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 consider a generalization of the diffusion equation on graphs. This generalized diffusion equation gives rise to both normal and superdiffusive processes on infinite one-dimensional graphs. The generalization is based on the $k$-path Laplacian operators $L_{k}$, which account for the hop of a diffusive particle to non-nearest neighbours in a graph. We first prove that the $k$-path Laplacian operators are self-adjoint. Then, we study the transformed $k$-path Laplacian operators using Laplace, factorial and Mellin transforms. We prove that the generalized diffusion equation using the Laplace-","authors_text":"Ehsan Hameed, Ernesto Estrada, Matthias Langer, Naomichi Hatano","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-04-02T20:24:20Z","title":"Path Laplacian operators and superdiffusive processes on graphs. I. One-dimensional case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.00555","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":"sha256:9dfc6117bb5e49f86298a56171e4b7b759055551ed6e6ebeb9706751c46ae504","target":"record","created_at":"2026-05-18T00:47:43Z","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":"a02b478f85cea5a9d2680be95f712d583f8dae7157f7b01619f449f70cf2f383","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-04-02T20:24:20Z","title_canon_sha256":"ad36c759a59de01b8eb39160937ecd26f4d1d7851bb28c05ec4fd6c7ddbd4b08"},"schema_version":"1.0","source":{"id":"1604.00555","kind":"arxiv","version":4}},"canonical_sha256":"fda130d17b67acefba1133db64d722994d04d0ba26a7e805db970a49902fd3e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fda130d17b67acefba1133db64d722994d04d0ba26a7e805db970a49902fd3e3","first_computed_at":"2026-05-18T00:47:43.014023Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:43.014023Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Pd744rWUugNYG3RKiU6bjKLtY7lyH9q2BtZiVqB9jvX1gu4uJ7Tzv2S/FqvoYbr3z0hsk2X9eKU3xpqmu2TsDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:43.014779Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.00555","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9dfc6117bb5e49f86298a56171e4b7b759055551ed6e6ebeb9706751c46ae504","sha256:74ac2e306504f90dd51dd669b8eed9dd50787512e8fb3cafc974a68406f24eb0"],"state_sha256":"c64b50bee3b621d5cc8ac7fc1c9061a49f7f569ec137908964926f75c9b3861c"}