{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:LMYVHT6RJRVI523FIKUOK4B3GL","short_pith_number":"pith:LMYVHT6R","schema_version":"1.0","canonical_sha256":"5b3153cfd14c6a8eeb6542a8e5703b32c01bb3d182a40197cdc9e7174ec19818","source":{"kind":"arxiv","id":"1303.6911","version":1},"attestation_state":"computed","paper":{"title":"Intrinsically knotted graphs with 21 edges","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GT","authors_text":"Jamison Barsotti, Thomas W. Mattman","submitted_at":"2013-03-27T17:48:59Z","abstract_excerpt":"We show that the 14 graphs obtained by $\\nabla\\mathrm{Y}$ moves on K_7 constitute a complete list of the minor minimal intrinsically knotted graphs on 21 edges. We also present evidence in support of a conjecture that the 20 graph Heawood family, obtained by a combination of $\\nabla\\mathrm{Y}$ and $\\mathrm{Y}\\nabla$ moves on K_7, is the list of graphs of size 21 that are minor minimal with respect to the property not 2--apex."},"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":"1303.6911","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-03-27T17:48:59Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"d394cb5a487b4499c8233ec806567d32e044f2ae586518f529993cc1f02b1e92","abstract_canon_sha256":"2f5ba24e4524ff7d7ef79dc98a394a3332aaeff80c98c06778a126dbcf591b64"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:39.337634Z","signature_b64":"wbkp7tlvK6/MvU6Rau90tx85lp5rcHsYRD0dY80vbQgHfJr/rvFXOgRgSB8xp7waDV4honFNBye25Z5wvm/iCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b3153cfd14c6a8eeb6542a8e5703b32c01bb3d182a40197cdc9e7174ec19818","last_reissued_at":"2026-05-18T03:29:39.336958Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:39.336958Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Intrinsically knotted graphs with 21 edges","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GT","authors_text":"Jamison Barsotti, Thomas W. Mattman","submitted_at":"2013-03-27T17:48:59Z","abstract_excerpt":"We show that the 14 graphs obtained by $\\nabla\\mathrm{Y}$ moves on K_7 constitute a complete list of the minor minimal intrinsically knotted graphs on 21 edges. We also present evidence in support of a conjecture that the 20 graph Heawood family, obtained by a combination of $\\nabla\\mathrm{Y}$ and $\\mathrm{Y}\\nabla$ moves on K_7, is the list of graphs of size 21 that are minor minimal with respect to the property not 2--apex."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6911","kind":"arxiv","version":1},"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":"1303.6911","created_at":"2026-05-18T03:29:39.337052+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.6911v1","created_at":"2026-05-18T03:29:39.337052+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.6911","created_at":"2026-05-18T03:29:39.337052+00:00"},{"alias_kind":"pith_short_12","alias_value":"LMYVHT6RJRVI","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_16","alias_value":"LMYVHT6RJRVI523F","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_8","alias_value":"LMYVHT6R","created_at":"2026-05-18T12:27:51.066281+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/LMYVHT6RJRVI523FIKUOK4B3GL","json":"https://pith.science/pith/LMYVHT6RJRVI523FIKUOK4B3GL.json","graph_json":"https://pith.science/api/pith-number/LMYVHT6RJRVI523FIKUOK4B3GL/graph.json","events_json":"https://pith.science/api/pith-number/LMYVHT6RJRVI523FIKUOK4B3GL/events.json","paper":"https://pith.science/paper/LMYVHT6R"},"agent_actions":{"view_html":"https://pith.science/pith/LMYVHT6RJRVI523FIKUOK4B3GL","download_json":"https://pith.science/pith/LMYVHT6RJRVI523FIKUOK4B3GL.json","view_paper":"https://pith.science/paper/LMYVHT6R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.6911&json=true","fetch_graph":"https://pith.science/api/pith-number/LMYVHT6RJRVI523FIKUOK4B3GL/graph.json","fetch_events":"https://pith.science/api/pith-number/LMYVHT6RJRVI523FIKUOK4B3GL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LMYVHT6RJRVI523FIKUOK4B3GL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LMYVHT6RJRVI523FIKUOK4B3GL/action/storage_attestation","attest_author":"https://pith.science/pith/LMYVHT6RJRVI523FIKUOK4B3GL/action/author_attestation","sign_citation":"https://pith.science/pith/LMYVHT6RJRVI523FIKUOK4B3GL/action/citation_signature","submit_replication":"https://pith.science/pith/LMYVHT6RJRVI523FIKUOK4B3GL/action/replication_record"}},"created_at":"2026-05-18T03:29:39.337052+00:00","updated_at":"2026-05-18T03:29:39.337052+00:00"}