{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:ULFD3GCXZPFPGOYP4NABCU6FJW","short_pith_number":"pith:ULFD3GCX","canonical_record":{"source":{"id":"2507.03244","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-07-04T01:34:26Z","cross_cats_sorted":[],"title_canon_sha256":"476ccf90f18457057c0a3e43c4668774fca646d4b8da0d6b9bedf91c8b2b8805","abstract_canon_sha256":"03b5202464d02b5d7c2132a1f9a9891d74f67b3941f7f815b44829abc33b53c3"},"schema_version":"1.0"},"canonical_sha256":"a2ca3d9857cbcaf33b0fe3401153c54d9330cf097fb0a4ce8ee8d96313bef4f0","source":{"kind":"arxiv","id":"2507.03244","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.03244","created_at":"2026-07-05T11:31:55Z"},{"alias_kind":"arxiv_version","alias_value":"2507.03244v1","created_at":"2026-07-05T11:31:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.03244","created_at":"2026-07-05T11:31:55Z"},{"alias_kind":"pith_short_12","alias_value":"ULFD3GCXZPFP","created_at":"2026-07-05T11:31:55Z"},{"alias_kind":"pith_short_16","alias_value":"ULFD3GCXZPFPGOYP","created_at":"2026-07-05T11:31:55Z"},{"alias_kind":"pith_short_8","alias_value":"ULFD3GCX","created_at":"2026-07-05T11:31:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:ULFD3GCXZPFPGOYP4NABCU6FJW","target":"record","payload":{"canonical_record":{"source":{"id":"2507.03244","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-07-04T01:34:26Z","cross_cats_sorted":[],"title_canon_sha256":"476ccf90f18457057c0a3e43c4668774fca646d4b8da0d6b9bedf91c8b2b8805","abstract_canon_sha256":"03b5202464d02b5d7c2132a1f9a9891d74f67b3941f7f815b44829abc33b53c3"},"schema_version":"1.0"},"canonical_sha256":"a2ca3d9857cbcaf33b0fe3401153c54d9330cf097fb0a4ce8ee8d96313bef4f0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:31:55.508808Z","signature_b64":"TKR7CdbaWxWx8osZGwkJaFt2q9iJGPPckyOwxK4JTSt9XKs8kDXAayAyIcm10hhayF5CGZ44pkcbnz/0A0p2Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2ca3d9857cbcaf33b0fe3401153c54d9330cf097fb0a4ce8ee8d96313bef4f0","last_reissued_at":"2026-07-05T11:31:55.508342Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:31:55.508342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.03244","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:31:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lkupS39w/L3bHqtYnc4Hron9IIqzKWo/w2FOQ64T7kbO2ff/DicDqELYprhS5RCWs15HDRrOWg6GtdOguZekDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T08:16:27.216144Z"},"content_sha256":"1e5f503d4ec9aaf3d028c56e6b7c0f9f2b6d00218eb2c30391e1df438a511774","schema_version":"1.0","event_id":"sha256:1e5f503d4ec9aaf3d028c56e6b7c0f9f2b6d00218eb2c30391e1df438a511774"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:ULFD3GCXZPFPGOYP4NABCU6FJW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Every graph with no $K_7^{\\vee}$-minor is $6$-colorable","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Agnes Totschnig, Sergey Norin","submitted_at":"2025-07-04T01:34:26Z","abstract_excerpt":"Let $K_7^{\\vee}$ denote the graph obtained from the complete graph on seven vertices by deleting two edges with a common end. Motivated by Hadwiger's conjecture, we prove that every graph with no $K_7^{\\vee}$-minor is $6$-colorable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.03244","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.03244/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:31:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kKYCkS8yYvwcsckYsTydAjyWwAs/4eq+Z9+LWBUVXQMPg0C854OU6fMBhFj1gP4OqAow5v/P2bBneXwgAUSNBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T08:16:27.216661Z"},"content_sha256":"841745fe5b2ccc5268c2200585d244ffc81a4cce31ab799c8a83bc754c132f5c","schema_version":"1.0","event_id":"sha256:841745fe5b2ccc5268c2200585d244ffc81a4cce31ab799c8a83bc754c132f5c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ULFD3GCXZPFPGOYP4NABCU6FJW/bundle.json","state_url":"https://pith.science/pith/ULFD3GCXZPFPGOYP4NABCU6FJW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ULFD3GCXZPFPGOYP4NABCU6FJW/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":"2026-08-14T08:16:27Z","links":{"resolver":"https://pith.science/pith/ULFD3GCXZPFPGOYP4NABCU6FJW","bundle":"https://pith.science/pith/ULFD3GCXZPFPGOYP4NABCU6FJW/bundle.json","state":"https://pith.science/pith/ULFD3GCXZPFPGOYP4NABCU6FJW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ULFD3GCXZPFPGOYP4NABCU6FJW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:ULFD3GCXZPFPGOYP4NABCU6FJW","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":"03b5202464d02b5d7c2132a1f9a9891d74f67b3941f7f815b44829abc33b53c3","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-07-04T01:34:26Z","title_canon_sha256":"476ccf90f18457057c0a3e43c4668774fca646d4b8da0d6b9bedf91c8b2b8805"},"schema_version":"1.0","source":{"id":"2507.03244","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.03244","created_at":"2026-07-05T11:31:55Z"},{"alias_kind":"arxiv_version","alias_value":"2507.03244v1","created_at":"2026-07-05T11:31:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.03244","created_at":"2026-07-05T11:31:55Z"},{"alias_kind":"pith_short_12","alias_value":"ULFD3GCXZPFP","created_at":"2026-07-05T11:31:55Z"},{"alias_kind":"pith_short_16","alias_value":"ULFD3GCXZPFPGOYP","created_at":"2026-07-05T11:31:55Z"},{"alias_kind":"pith_short_8","alias_value":"ULFD3GCX","created_at":"2026-07-05T11:31:55Z"}],"graph_snapshots":[{"event_id":"sha256:841745fe5b2ccc5268c2200585d244ffc81a4cce31ab799c8a83bc754c132f5c","target":"graph","created_at":"2026-07-05T11:31:55Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2507.03244/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $K_7^{\\vee}$ denote the graph obtained from the complete graph on seven vertices by deleting two edges with a common end. Motivated by Hadwiger's conjecture, we prove that every graph with no $K_7^{\\vee}$-minor is $6$-colorable.","authors_text":"Agnes Totschnig, Sergey Norin","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-07-04T01:34:26Z","title":"Every graph with no $K_7^{\\vee}$-minor is $6$-colorable"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.03244","kind":"arxiv","version":1},"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":"sha256:1e5f503d4ec9aaf3d028c56e6b7c0f9f2b6d00218eb2c30391e1df438a511774","target":"record","created_at":"2026-07-05T11:31:55Z","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":"03b5202464d02b5d7c2132a1f9a9891d74f67b3941f7f815b44829abc33b53c3","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-07-04T01:34:26Z","title_canon_sha256":"476ccf90f18457057c0a3e43c4668774fca646d4b8da0d6b9bedf91c8b2b8805"},"schema_version":"1.0","source":{"id":"2507.03244","kind":"arxiv","version":1}},"canonical_sha256":"a2ca3d9857cbcaf33b0fe3401153c54d9330cf097fb0a4ce8ee8d96313bef4f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2ca3d9857cbcaf33b0fe3401153c54d9330cf097fb0a4ce8ee8d96313bef4f0","first_computed_at":"2026-07-05T11:31:55.508342Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:31:55.508342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TKR7CdbaWxWx8osZGwkJaFt2q9iJGPPckyOwxK4JTSt9XKs8kDXAayAyIcm10hhayF5CGZ44pkcbnz/0A0p2Dg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:31:55.508808Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.03244","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e5f503d4ec9aaf3d028c56e6b7c0f9f2b6d00218eb2c30391e1df438a511774","sha256:841745fe5b2ccc5268c2200585d244ffc81a4cce31ab799c8a83bc754c132f5c"],"state_sha256":"1805c5c41fc0e0f132aec95f6f4636dac2210cf89c3b7b40d3576c4219d23f86"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XIZHOe9bjHqhQFWf9nx4WGIWJ48xqArrdmNGIuew0K27EOcIXshVn3sgk0Kj5zYihJ42PnevVUiwAAJRYt7CDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T08:16:27.224160Z","bundle_sha256":"aa098229e4136119ffb66d420e1289914ca5f7f7a446d61571883f71b1ff6bf0"}}