{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:GJPD7AKTJBWP57G3SA22FFLP5R","short_pith_number":"pith:GJPD7AKT","schema_version":"1.0","canonical_sha256":"325e3f8153486cfefcdb9035a2956fec4f6df24b490488adacd0c2cc4ff02f68","source":{"kind":"arxiv","id":"1301.4121","version":2},"attestation_state":"computed","paper":{"title":"An algebraic formulation of the graph reconstruction conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Bhalchandra D. Thatte, Igor C. Oliveira","submitted_at":"2013-01-17T15:25:55Z","abstract_excerpt":"The graph reconstruction conjecture asserts that every finite simple graph on at least three vertices can be reconstructed up to isomorphism from its deck - the collection of its vertex-deleted subgraphs. Kocay's Lemma is an important tool in graph reconstruction. Roughly speaking, given the deck of a graph $G$ and any finite sequence of graphs, it gives a linear constraint that every reconstruction of $G$ must satisfy.\n  Let $\\psi(n)$ be the number of distinct (mutually non-isomorphic) graphs on $n$ vertices, and let $d(n)$ be the number of distinct decks that can be constructed from these gr"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1301.4121","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-17T15:25:55Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"d9f7348a5f4ea0cf66edd0de40361b208d02061398fc945354173b6b8cea6214","abstract_canon_sha256":"d172659dc7525b57f8ae622e3bad860b415a9499436775f391d8b0c4ae9cfb26"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:24.494232Z","signature_b64":"RDb0mvZqYeNICc6vs5qOIWFKB59DtChwgR7BeIbZAwbc/+Xsuv16cKPCy6gaq8ujIyFjga6S0uWjGZNQTZFkDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"325e3f8153486cfefcdb9035a2956fec4f6df24b490488adacd0c2cc4ff02f68","last_reissued_at":"2026-05-18T02:43:24.493736Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:24.493736Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An algebraic formulation of the graph reconstruction conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Bhalchandra D. Thatte, Igor C. Oliveira","submitted_at":"2013-01-17T15:25:55Z","abstract_excerpt":"The graph reconstruction conjecture asserts that every finite simple graph on at least three vertices can be reconstructed up to isomorphism from its deck - the collection of its vertex-deleted subgraphs. Kocay's Lemma is an important tool in graph reconstruction. Roughly speaking, given the deck of a graph $G$ and any finite sequence of graphs, it gives a linear constraint that every reconstruction of $G$ must satisfy.\n  Let $\\psi(n)$ be the number of distinct (mutually non-isomorphic) graphs on $n$ vertices, and let $d(n)$ be the number of distinct decks that can be constructed from these gr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4121","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1301.4121","created_at":"2026-05-18T02:43:24.493807+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.4121v2","created_at":"2026-05-18T02:43:24.493807+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.4121","created_at":"2026-05-18T02:43:24.493807+00:00"},{"alias_kind":"pith_short_12","alias_value":"GJPD7AKTJBWP","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_16","alias_value":"GJPD7AKTJBWP57G3","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_8","alias_value":"GJPD7AKT","created_at":"2026-05-18T12:27:45.050594+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GJPD7AKTJBWP57G3SA22FFLP5R","json":"https://pith.science/pith/GJPD7AKTJBWP57G3SA22FFLP5R.json","graph_json":"https://pith.science/api/pith-number/GJPD7AKTJBWP57G3SA22FFLP5R/graph.json","events_json":"https://pith.science/api/pith-number/GJPD7AKTJBWP57G3SA22FFLP5R/events.json","paper":"https://pith.science/paper/GJPD7AKT"},"agent_actions":{"view_html":"https://pith.science/pith/GJPD7AKTJBWP57G3SA22FFLP5R","download_json":"https://pith.science/pith/GJPD7AKTJBWP57G3SA22FFLP5R.json","view_paper":"https://pith.science/paper/GJPD7AKT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.4121&json=true","fetch_graph":"https://pith.science/api/pith-number/GJPD7AKTJBWP57G3SA22FFLP5R/graph.json","fetch_events":"https://pith.science/api/pith-number/GJPD7AKTJBWP57G3SA22FFLP5R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GJPD7AKTJBWP57G3SA22FFLP5R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GJPD7AKTJBWP57G3SA22FFLP5R/action/storage_attestation","attest_author":"https://pith.science/pith/GJPD7AKTJBWP57G3SA22FFLP5R/action/author_attestation","sign_citation":"https://pith.science/pith/GJPD7AKTJBWP57G3SA22FFLP5R/action/citation_signature","submit_replication":"https://pith.science/pith/GJPD7AKTJBWP57G3SA22FFLP5R/action/replication_record"}},"created_at":"2026-05-18T02:43:24.493807+00:00","updated_at":"2026-05-18T02:43:24.493807+00:00"}