{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:KCLJ7IGNVAAAZMRV3MWOIFADEV","short_pith_number":"pith:KCLJ7IGN","schema_version":"1.0","canonical_sha256":"50969fa0cda8000cb235db2ce41403254b62543feb62f75adc23b137c2435f66","source":{"kind":"arxiv","id":"1401.6552","version":1},"attestation_state":"computed","paper":{"title":"Unstable Graphs: A Fresh Outlook via TF-Automorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Josef Lauri, Raffaele Scapellato, Russell Mizzi","submitted_at":"2014-01-25T15:52:24Z","abstract_excerpt":"In this paper, we first establish the very close link between stability of graphs, a concept first introduced in \\cite{Scapsalvi1} and studied most notably by Surowski \\cite{Surowski1}, \\cite{Surowski2} and Wilson \\cite{Wilson01} and two-fold automorphisms. The concept of two-fold isomorphisms, as far as we know, first appeared in literature in the form of isotopies of digraphs \\cite{zelinka4}, \\cite{zelinka1}, \\cite{zelinka2}, \\cite{zelinka3} and later studied formally in \\cite{lms1}, \\cite{lms2} with a greater emphasis on undirected graphs. We then turn our attention to the stability of grap"},"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":"1401.6552","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-01-25T15:52:24Z","cross_cats_sorted":[],"title_canon_sha256":"c2221f0519890b480a714e8c066355aa2cac09b67ddb79532efb409de90c3ec8","abstract_canon_sha256":"0d7ef62043890cc1f80ce646f60f582e1b2bc67cf66f3c7a724ef0cfcea96879"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:01.384795Z","signature_b64":"lhS+rEmgJLDobE7eqn5J4B1WjAWvqBEU9+xDAV4c4Gxe/3uPxn8G7173THKohDU1xX1Dyh6hmc+B46ZdGOaSDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"50969fa0cda8000cb235db2ce41403254b62543feb62f75adc23b137c2435f66","last_reissued_at":"2026-05-18T03:01:01.384151Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:01.384151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Unstable Graphs: A Fresh Outlook via TF-Automorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Josef Lauri, Raffaele Scapellato, Russell Mizzi","submitted_at":"2014-01-25T15:52:24Z","abstract_excerpt":"In this paper, we first establish the very close link between stability of graphs, a concept first introduced in \\cite{Scapsalvi1} and studied most notably by Surowski \\cite{Surowski1}, \\cite{Surowski2} and Wilson \\cite{Wilson01} and two-fold automorphisms. The concept of two-fold isomorphisms, as far as we know, first appeared in literature in the form of isotopies of digraphs \\cite{zelinka4}, \\cite{zelinka1}, \\cite{zelinka2}, \\cite{zelinka3} and later studied formally in \\cite{lms1}, \\cite{lms2} with a greater emphasis on undirected graphs. We then turn our attention to the stability of grap"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6552","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":"1401.6552","created_at":"2026-05-18T03:01:01.384240+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.6552v1","created_at":"2026-05-18T03:01:01.384240+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.6552","created_at":"2026-05-18T03:01:01.384240+00:00"},{"alias_kind":"pith_short_12","alias_value":"KCLJ7IGNVAAA","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_16","alias_value":"KCLJ7IGNVAAAZMRV","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_8","alias_value":"KCLJ7IGN","created_at":"2026-05-18T12:28:35.611951+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/KCLJ7IGNVAAAZMRV3MWOIFADEV","json":"https://pith.science/pith/KCLJ7IGNVAAAZMRV3MWOIFADEV.json","graph_json":"https://pith.science/api/pith-number/KCLJ7IGNVAAAZMRV3MWOIFADEV/graph.json","events_json":"https://pith.science/api/pith-number/KCLJ7IGNVAAAZMRV3MWOIFADEV/events.json","paper":"https://pith.science/paper/KCLJ7IGN"},"agent_actions":{"view_html":"https://pith.science/pith/KCLJ7IGNVAAAZMRV3MWOIFADEV","download_json":"https://pith.science/pith/KCLJ7IGNVAAAZMRV3MWOIFADEV.json","view_paper":"https://pith.science/paper/KCLJ7IGN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.6552&json=true","fetch_graph":"https://pith.science/api/pith-number/KCLJ7IGNVAAAZMRV3MWOIFADEV/graph.json","fetch_events":"https://pith.science/api/pith-number/KCLJ7IGNVAAAZMRV3MWOIFADEV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KCLJ7IGNVAAAZMRV3MWOIFADEV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KCLJ7IGNVAAAZMRV3MWOIFADEV/action/storage_attestation","attest_author":"https://pith.science/pith/KCLJ7IGNVAAAZMRV3MWOIFADEV/action/author_attestation","sign_citation":"https://pith.science/pith/KCLJ7IGNVAAAZMRV3MWOIFADEV/action/citation_signature","submit_replication":"https://pith.science/pith/KCLJ7IGNVAAAZMRV3MWOIFADEV/action/replication_record"}},"created_at":"2026-05-18T03:01:01.384240+00:00","updated_at":"2026-05-18T03:01:01.384240+00:00"}