{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:S3Q32WAYM4HRFKQRVGOME6PAMK","short_pith_number":"pith:S3Q32WAY","canonical_record":{"source":{"id":"1801.00179","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-30T19:08:38Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"8d417732f7e9c830caaa485ec9b5e93d1cce3bd51a397651a85b3a890e556ef3","abstract_canon_sha256":"d29e378f6252d58e46bc67dd21551c1595adc7e4106c6b5409e1c6100f873448"},"schema_version":"1.0"},"canonical_sha256":"96e1bd5818670f12aa11a99cc279e062a7648c676b1b777e996dd71b39a4eca5","source":{"kind":"arxiv","id":"1801.00179","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.00179","created_at":"2026-05-18T00:14:34Z"},{"alias_kind":"arxiv_version","alias_value":"1801.00179v2","created_at":"2026-05-18T00:14:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.00179","created_at":"2026-05-18T00:14:34Z"},{"alias_kind":"pith_short_12","alias_value":"S3Q32WAYM4HR","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"S3Q32WAYM4HRFKQR","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"S3Q32WAY","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:S3Q32WAYM4HRFKQRVGOME6PAMK","target":"record","payload":{"canonical_record":{"source":{"id":"1801.00179","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-30T19:08:38Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"8d417732f7e9c830caaa485ec9b5e93d1cce3bd51a397651a85b3a890e556ef3","abstract_canon_sha256":"d29e378f6252d58e46bc67dd21551c1595adc7e4106c6b5409e1c6100f873448"},"schema_version":"1.0"},"canonical_sha256":"96e1bd5818670f12aa11a99cc279e062a7648c676b1b777e996dd71b39a4eca5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:34.140194Z","signature_b64":"XU+5zT6nBMYstFF9SBdjK9d+YVPihNMlXpMHQcWLmwZmp2paJWOtTSRZsIFjIn0TLGzD5WVapoNjXEDnvG0mBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96e1bd5818670f12aa11a99cc279e062a7648c676b1b777e996dd71b39a4eca5","last_reissued_at":"2026-05-18T00:14:34.139637Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:34.139637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.00179","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:14:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xAjfwf17FjQnWv8S7ylh8swSvQk/yxq5a31qv/YoMoErTpLsYRNS0IClfjQzyZBcpt/EgFAEUSWPAavQ/rASCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T20:41:46.439042Z"},"content_sha256":"31cdcd387d82cf764a56b9d00a3b34e0201e8befc984f530f09bf202ca62dadb","schema_version":"1.0","event_id":"sha256:31cdcd387d82cf764a56b9d00a3b34e0201e8befc984f530f09bf202ca62dadb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:S3Q32WAYM4HRFKQRVGOME6PAMK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"n-Arc Connected Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.CO","authors_text":"Ana Mamatelashvili, Max Pitz, Paul Gartside","submitted_at":"2017-12-30T19:08:38Z","abstract_excerpt":"Given a graph G, of arbitrary size and unbounded vertex degree, denote by |G| the one-complex associated with $G$. The topological space |G| is n-arc connected (n-ac) if every set of no more than n points of |G| are contained in an arc (a homeomorphic copy of the closed unit interval).\n  For any graph G, we show the following are equivalent: (i) |G| in 7-ac, (ii) |G| is n-ac for all n, and (iii) G is a subdivision of one of nine graphs. A graph G has |G| 6-ac if and only if either G is one of the nine 7-ac graphs, or, after suppressing all degree-2-vertices, the graph G is 3-regular, 3-connect"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00179","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:14:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y5RegJLXJb9l07/Y8axTayxIkUVfsXuoySW2uLfvmwqTipbx6FdncdvXOkgWtd7iOtFfzGAIqhbXke/ph9BVCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T20:41:46.439388Z"},"content_sha256":"273830e1e6dc45e21a76040d818a4e5eb01503445a61718f4041546cdce0f947","schema_version":"1.0","event_id":"sha256:273830e1e6dc45e21a76040d818a4e5eb01503445a61718f4041546cdce0f947"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S3Q32WAYM4HRFKQRVGOME6PAMK/bundle.json","state_url":"https://pith.science/pith/S3Q32WAYM4HRFKQRVGOME6PAMK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S3Q32WAYM4HRFKQRVGOME6PAMK/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":"2026-06-20T20:41:46Z","links":{"resolver":"https://pith.science/pith/S3Q32WAYM4HRFKQRVGOME6PAMK","bundle":"https://pith.science/pith/S3Q32WAYM4HRFKQRVGOME6PAMK/bundle.json","state":"https://pith.science/pith/S3Q32WAYM4HRFKQRVGOME6PAMK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S3Q32WAYM4HRFKQRVGOME6PAMK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:S3Q32WAYM4HRFKQRVGOME6PAMK","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":"d29e378f6252d58e46bc67dd21551c1595adc7e4106c6b5409e1c6100f873448","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-30T19:08:38Z","title_canon_sha256":"8d417732f7e9c830caaa485ec9b5e93d1cce3bd51a397651a85b3a890e556ef3"},"schema_version":"1.0","source":{"id":"1801.00179","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.00179","created_at":"2026-05-18T00:14:34Z"},{"alias_kind":"arxiv_version","alias_value":"1801.00179v2","created_at":"2026-05-18T00:14:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.00179","created_at":"2026-05-18T00:14:34Z"},{"alias_kind":"pith_short_12","alias_value":"S3Q32WAYM4HR","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"S3Q32WAYM4HRFKQR","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"S3Q32WAY","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:273830e1e6dc45e21a76040d818a4e5eb01503445a61718f4041546cdce0f947","target":"graph","created_at":"2026-05-18T00:14:34Z","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":"Given a graph G, of arbitrary size and unbounded vertex degree, denote by |G| the one-complex associated with $G$. The topological space |G| is n-arc connected (n-ac) if every set of no more than n points of |G| are contained in an arc (a homeomorphic copy of the closed unit interval).\n  For any graph G, we show the following are equivalent: (i) |G| in 7-ac, (ii) |G| is n-ac for all n, and (iii) G is a subdivision of one of nine graphs. A graph G has |G| 6-ac if and only if either G is one of the nine 7-ac graphs, or, after suppressing all degree-2-vertices, the graph G is 3-regular, 3-connect","authors_text":"Ana Mamatelashvili, Max Pitz, Paul Gartside","cross_cats":["math.GN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-30T19:08:38Z","title":"n-Arc Connected Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00179","kind":"arxiv","version":2},"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":"sha256:31cdcd387d82cf764a56b9d00a3b34e0201e8befc984f530f09bf202ca62dadb","target":"record","created_at":"2026-05-18T00:14:34Z","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":"d29e378f6252d58e46bc67dd21551c1595adc7e4106c6b5409e1c6100f873448","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-30T19:08:38Z","title_canon_sha256":"8d417732f7e9c830caaa485ec9b5e93d1cce3bd51a397651a85b3a890e556ef3"},"schema_version":"1.0","source":{"id":"1801.00179","kind":"arxiv","version":2}},"canonical_sha256":"96e1bd5818670f12aa11a99cc279e062a7648c676b1b777e996dd71b39a4eca5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"96e1bd5818670f12aa11a99cc279e062a7648c676b1b777e996dd71b39a4eca5","first_computed_at":"2026-05-18T00:14:34.139637Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:34.139637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XU+5zT6nBMYstFF9SBdjK9d+YVPihNMlXpMHQcWLmwZmp2paJWOtTSRZsIFjIn0TLGzD5WVapoNjXEDnvG0mBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:34.140194Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.00179","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31cdcd387d82cf764a56b9d00a3b34e0201e8befc984f530f09bf202ca62dadb","sha256:273830e1e6dc45e21a76040d818a4e5eb01503445a61718f4041546cdce0f947"],"state_sha256":"df5999c6408d4743d234c0100addc135f98cd3a18c834864798c42104c80d773"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gR/WjWUlFBKj1G73KIUQeSp2Oe1sVkSL+/TAcnsFdl0NL/XinLks5+VJuiT9cf37251+iNtv+0bWe0pi+Hl3Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T20:41:46.441195Z","bundle_sha256":"9be127a2ccb782346144d46902c8f49caa83bfb531abc612ec02a63b756e5493"}}