{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:IXTDZS2N5J2FUQ6V5M4UGIHM5N","short_pith_number":"pith:IXTDZS2N","canonical_record":{"source":{"id":"2503.07447","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-03-10T15:27:26Z","cross_cats_sorted":["cs.DM","math-ph","math.MP"],"title_canon_sha256":"877b7f49924e3bd17b8d8d1d5fb5583267aac84fded6e9c1d775a1e70bba8c7d","abstract_canon_sha256":"a97b1eb26d725dc06ca01b0fe6ed12f0feeb236db65d3baefd1efde6485a0547"},"schema_version":"1.0"},"canonical_sha256":"45e63ccb4dea745a43d5eb394320eceb508b738eb16428f60d401dc1323e3449","source":{"kind":"arxiv","id":"2503.07447","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.07447","created_at":"2026-07-05T10:27:56Z"},{"alias_kind":"arxiv_version","alias_value":"2503.07447v1","created_at":"2026-07-05T10:27:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.07447","created_at":"2026-07-05T10:27:56Z"},{"alias_kind":"pith_short_12","alias_value":"IXTDZS2N5J2F","created_at":"2026-07-05T10:27:56Z"},{"alias_kind":"pith_short_16","alias_value":"IXTDZS2N5J2FUQ6V","created_at":"2026-07-05T10:27:56Z"},{"alias_kind":"pith_short_8","alias_value":"IXTDZS2N","created_at":"2026-07-05T10:27:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:IXTDZS2N5J2FUQ6V5M4UGIHM5N","target":"record","payload":{"canonical_record":{"source":{"id":"2503.07447","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-03-10T15:27:26Z","cross_cats_sorted":["cs.DM","math-ph","math.MP"],"title_canon_sha256":"877b7f49924e3bd17b8d8d1d5fb5583267aac84fded6e9c1d775a1e70bba8c7d","abstract_canon_sha256":"a97b1eb26d725dc06ca01b0fe6ed12f0feeb236db65d3baefd1efde6485a0547"},"schema_version":"1.0"},"canonical_sha256":"45e63ccb4dea745a43d5eb394320eceb508b738eb16428f60d401dc1323e3449","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:27:56.464843Z","signature_b64":"fupO1TdM1G7T79lhl9PwnmMwpQ3Znp6XSIoFZ/s9/PJuYsWyUp6Li2I3ZSjyz1EKtQibKu/O7zMhNh+yhuMFCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"45e63ccb4dea745a43d5eb394320eceb508b738eb16428f60d401dc1323e3449","last_reissued_at":"2026-07-05T10:27:56.464091Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:27:56.464091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2503.07447","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":"2026-07-05T10:27:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sWlpa2Ki5xsfMIsE8PpXd1XhQI32Cum6GDcxObFLRjZEfVk9Wgrt7F87ud5NxoqN4GzTnmd/9Hj5/5gFzuHhCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T02:39:28.487558Z"},"content_sha256":"2cba08da45d204a93ef4f64ed00fd979122c65168233536f9ecd9cc278583992","schema_version":"1.0","event_id":"sha256:2cba08da45d204a93ef4f64ed00fd979122c65168233536f9ecd9cc278583992"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:IXTDZS2N5J2FUQ6V5M4UGIHM5N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A new density limit for unanimity in majority dynamics on random graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM","math-ph","math.MP"],"primary_cat":"math.CO","authors_text":"BaoLinh Tran, Jeong Han Kim","submitted_at":"2025-03-10T15:27:26Z","abstract_excerpt":"Majority dynamics is a process on a simple, undirected graph $G$ with an initial Red/Blue color for every vertex of $G$. Each day, each vertex updates its color following the majority among its neighbors, using its previous color for tie-breaking. The dynamics achieves \\textit{unanimity} if every vertex has the same color after finitely many days, and such color is said to \\textit{win}.\n  When $G$ is a $G(n,p)$ random graph, L. Tran and Vu (2019) found a codition in terms of $p$ and the initial difference $2\\Delta$ beteween the sizes of the Red and Blue camps, such that unanimity is achieved w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.07447","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/2503.07447/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":"2026-07-05T10:27:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cdQauX7NyHezZfWvUq0xxImuzRFEVzIw7HIz7nLz1ddoBYx8IjkUWZlD0qLDRg0mKOSdY41YQzAE5y7laaAmDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T02:39:28.488079Z"},"content_sha256":"a52a974bb5776d6cc3d7e32826e61e3f2ea1634670839582c2fbe95cf02d5a44","schema_version":"1.0","event_id":"sha256:a52a974bb5776d6cc3d7e32826e61e3f2ea1634670839582c2fbe95cf02d5a44"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IXTDZS2N5J2FUQ6V5M4UGIHM5N/bundle.json","state_url":"https://pith.science/pith/IXTDZS2N5J2FUQ6V5M4UGIHM5N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IXTDZS2N5J2FUQ6V5M4UGIHM5N/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":"2026-08-09T02:39:28Z","links":{"resolver":"https://pith.science/pith/IXTDZS2N5J2FUQ6V5M4UGIHM5N","bundle":"https://pith.science/pith/IXTDZS2N5J2FUQ6V5M4UGIHM5N/bundle.json","state":"https://pith.science/pith/IXTDZS2N5J2FUQ6V5M4UGIHM5N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IXTDZS2N5J2FUQ6V5M4UGIHM5N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:IXTDZS2N5J2FUQ6V5M4UGIHM5N","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":"a97b1eb26d725dc06ca01b0fe6ed12f0feeb236db65d3baefd1efde6485a0547","cross_cats_sorted":["cs.DM","math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-03-10T15:27:26Z","title_canon_sha256":"877b7f49924e3bd17b8d8d1d5fb5583267aac84fded6e9c1d775a1e70bba8c7d"},"schema_version":"1.0","source":{"id":"2503.07447","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.07447","created_at":"2026-07-05T10:27:56Z"},{"alias_kind":"arxiv_version","alias_value":"2503.07447v1","created_at":"2026-07-05T10:27:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.07447","created_at":"2026-07-05T10:27:56Z"},{"alias_kind":"pith_short_12","alias_value":"IXTDZS2N5J2F","created_at":"2026-07-05T10:27:56Z"},{"alias_kind":"pith_short_16","alias_value":"IXTDZS2N5J2FUQ6V","created_at":"2026-07-05T10:27:56Z"},{"alias_kind":"pith_short_8","alias_value":"IXTDZS2N","created_at":"2026-07-05T10:27:56Z"}],"graph_snapshots":[{"event_id":"sha256:a52a974bb5776d6cc3d7e32826e61e3f2ea1634670839582c2fbe95cf02d5a44","target":"graph","created_at":"2026-07-05T10:27:56Z","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/2503.07447/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Majority dynamics is a process on a simple, undirected graph $G$ with an initial Red/Blue color for every vertex of $G$. Each day, each vertex updates its color following the majority among its neighbors, using its previous color for tie-breaking. The dynamics achieves \\textit{unanimity} if every vertex has the same color after finitely many days, and such color is said to \\textit{win}.\n  When $G$ is a $G(n,p)$ random graph, L. Tran and Vu (2019) found a codition in terms of $p$ and the initial difference $2\\Delta$ beteween the sizes of the Red and Blue camps, such that unanimity is achieved w","authors_text":"BaoLinh Tran, Jeong Han Kim","cross_cats":["cs.DM","math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-03-10T15:27:26Z","title":"A new density limit for unanimity in majority dynamics on random graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.07447","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":"sha256:2cba08da45d204a93ef4f64ed00fd979122c65168233536f9ecd9cc278583992","target":"record","created_at":"2026-07-05T10:27:56Z","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":"a97b1eb26d725dc06ca01b0fe6ed12f0feeb236db65d3baefd1efde6485a0547","cross_cats_sorted":["cs.DM","math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-03-10T15:27:26Z","title_canon_sha256":"877b7f49924e3bd17b8d8d1d5fb5583267aac84fded6e9c1d775a1e70bba8c7d"},"schema_version":"1.0","source":{"id":"2503.07447","kind":"arxiv","version":1}},"canonical_sha256":"45e63ccb4dea745a43d5eb394320eceb508b738eb16428f60d401dc1323e3449","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"45e63ccb4dea745a43d5eb394320eceb508b738eb16428f60d401dc1323e3449","first_computed_at":"2026-07-05T10:27:56.464091Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:27:56.464091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fupO1TdM1G7T79lhl9PwnmMwpQ3Znp6XSIoFZ/s9/PJuYsWyUp6Li2I3ZSjyz1EKtQibKu/O7zMhNh+yhuMFCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:27:56.464843Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.07447","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2cba08da45d204a93ef4f64ed00fd979122c65168233536f9ecd9cc278583992","sha256:a52a974bb5776d6cc3d7e32826e61e3f2ea1634670839582c2fbe95cf02d5a44"],"state_sha256":"a3519b332ca3dbdcd9f76f455bb4ab6366f8a6d570f2bf9cad7612c352ce3d6c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YebBm7PQrtug8e5Xls+NSwVX13f40af+oCzz6okroKrx3KCykZts+UIHu9yx6G+E5/3vzuQQIrOHZb1zvC6qAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T02:39:28.491766Z","bundle_sha256":"837e199a4b20744a5a94ba0fd0002f08be6eff17dfd64fb19ec0107c7bce07e3"}}