{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:NADAQ6IB6UNRKJSXORIX5W4CRI","short_pith_number":"pith:NADAQ6IB","canonical_record":{"source":{"id":"1102.2583","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-02-13T12:03:04Z","cross_cats_sorted":["math.CO","stat.TH"],"title_canon_sha256":"ca0445a0acf7dd1536b3e20c0d68f2e90fc180ed7b470de2ddc6ae790e9dffab","abstract_canon_sha256":"9d2890a6597d2f338d0aefa657c85c4807928ebadfcd5d02b81581736010492f"},"schema_version":"1.0"},"canonical_sha256":"6806087901f51b15265774517edb828a16cbdf81a5c5a2d1131357e5ef41c81b","source":{"kind":"arxiv","id":"1102.2583","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.2583","created_at":"2026-05-18T03:36:48Z"},{"alias_kind":"arxiv_version","alias_value":"1102.2583v3","created_at":"2026-05-18T03:36:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.2583","created_at":"2026-05-18T03:36:48Z"},{"alias_kind":"pith_short_12","alias_value":"NADAQ6IB6UNR","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NADAQ6IB6UNRKJSX","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NADAQ6IB","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:NADAQ6IB6UNRKJSXORIX5W4CRI","target":"record","payload":{"canonical_record":{"source":{"id":"1102.2583","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-02-13T12:03:04Z","cross_cats_sorted":["math.CO","stat.TH"],"title_canon_sha256":"ca0445a0acf7dd1536b3e20c0d68f2e90fc180ed7b470de2ddc6ae790e9dffab","abstract_canon_sha256":"9d2890a6597d2f338d0aefa657c85c4807928ebadfcd5d02b81581736010492f"},"schema_version":"1.0"},"canonical_sha256":"6806087901f51b15265774517edb828a16cbdf81a5c5a2d1131357e5ef41c81b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:48.356795Z","signature_b64":"3YcJwh4WeW5OsuaJpJwep1WKvcNa0CyJMbCRwDr2w7bjL40M5mITfxg3bzwdDXe8VQqlfwgGgcnv6gfjz9BCAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6806087901f51b15265774517edb828a16cbdf81a5c5a2d1131357e5ef41c81b","last_reissued_at":"2026-05-18T03:36:48.356219Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:48.356219Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.2583","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:36:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dxuNxQZENUvjP08hSZ2Mk777FzUnvbXB4Y9v/jNw2AtJy4E68fuz1Kg9JWAQibT9dOtYsZCrHLvQ9iM4dzu9Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T18:51:23.204382Z"},"content_sha256":"57485ac896b88e910ccd7d468121bac8edf158cd847236f58f840b80a5f8b1a7","schema_version":"1.0","event_id":"sha256:57485ac896b88e910ccd7d468121bac8edf158cd847236f58f840b80a5f8b1a7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:NADAQ6IB6UNRKJSXORIX5W4CRI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Graver basis for an undirected graph and its application to testing the beta model of random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","stat.TH"],"primary_cat":"math.ST","authors_text":"Akimichi Takemura, Hisayuki Hara, Mitsunori Ogawa","submitted_at":"2011-02-13T12:03:04Z","abstract_excerpt":"In this paper we give an explicit and algorithmic description of Graver basis for the toric ideal associated with a simple undirected graph and apply the basis for testing the beta model of random graphs by Markov chain Monte Carlo method."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.2583","kind":"arxiv","version":3},"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":"2026-05-18T03:36:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PQIvpgsNJjWaURb5ylY6oW05A9Cdm7pqb05wuNrikjK+62uoLnDGHJsf1Ik4V+ehVEafS4cjbHBXY7toNEKcBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T18:51:23.205035Z"},"content_sha256":"bf58e6a935cc22c30d16068254278efb0136a343be4e980263895dae23150d76","schema_version":"1.0","event_id":"sha256:bf58e6a935cc22c30d16068254278efb0136a343be4e980263895dae23150d76"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NADAQ6IB6UNRKJSXORIX5W4CRI/bundle.json","state_url":"https://pith.science/pith/NADAQ6IB6UNRKJSXORIX5W4CRI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NADAQ6IB6UNRKJSXORIX5W4CRI/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":"2026-05-26T18:51:23Z","links":{"resolver":"https://pith.science/pith/NADAQ6IB6UNRKJSXORIX5W4CRI","bundle":"https://pith.science/pith/NADAQ6IB6UNRKJSXORIX5W4CRI/bundle.json","state":"https://pith.science/pith/NADAQ6IB6UNRKJSXORIX5W4CRI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NADAQ6IB6UNRKJSXORIX5W4CRI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:NADAQ6IB6UNRKJSXORIX5W4CRI","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":"9d2890a6597d2f338d0aefa657c85c4807928ebadfcd5d02b81581736010492f","cross_cats_sorted":["math.CO","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-02-13T12:03:04Z","title_canon_sha256":"ca0445a0acf7dd1536b3e20c0d68f2e90fc180ed7b470de2ddc6ae790e9dffab"},"schema_version":"1.0","source":{"id":"1102.2583","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.2583","created_at":"2026-05-18T03:36:48Z"},{"alias_kind":"arxiv_version","alias_value":"1102.2583v3","created_at":"2026-05-18T03:36:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.2583","created_at":"2026-05-18T03:36:48Z"},{"alias_kind":"pith_short_12","alias_value":"NADAQ6IB6UNR","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NADAQ6IB6UNRKJSX","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NADAQ6IB","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:bf58e6a935cc22c30d16068254278efb0136a343be4e980263895dae23150d76","target":"graph","created_at":"2026-05-18T03:36:48Z","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":"In this paper we give an explicit and algorithmic description of Graver basis for the toric ideal associated with a simple undirected graph and apply the basis for testing the beta model of random graphs by Markov chain Monte Carlo method.","authors_text":"Akimichi Takemura, Hisayuki Hara, Mitsunori Ogawa","cross_cats":["math.CO","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-02-13T12:03:04Z","title":"Graver basis for an undirected graph and its application to testing the beta model of random graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.2583","kind":"arxiv","version":3},"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":"sha256:57485ac896b88e910ccd7d468121bac8edf158cd847236f58f840b80a5f8b1a7","target":"record","created_at":"2026-05-18T03:36:48Z","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":"9d2890a6597d2f338d0aefa657c85c4807928ebadfcd5d02b81581736010492f","cross_cats_sorted":["math.CO","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-02-13T12:03:04Z","title_canon_sha256":"ca0445a0acf7dd1536b3e20c0d68f2e90fc180ed7b470de2ddc6ae790e9dffab"},"schema_version":"1.0","source":{"id":"1102.2583","kind":"arxiv","version":3}},"canonical_sha256":"6806087901f51b15265774517edb828a16cbdf81a5c5a2d1131357e5ef41c81b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6806087901f51b15265774517edb828a16cbdf81a5c5a2d1131357e5ef41c81b","first_computed_at":"2026-05-18T03:36:48.356219Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:48.356219Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3YcJwh4WeW5OsuaJpJwep1WKvcNa0CyJMbCRwDr2w7bjL40M5mITfxg3bzwdDXe8VQqlfwgGgcnv6gfjz9BCAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:48.356795Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.2583","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57485ac896b88e910ccd7d468121bac8edf158cd847236f58f840b80a5f8b1a7","sha256:bf58e6a935cc22c30d16068254278efb0136a343be4e980263895dae23150d76"],"state_sha256":"6277bcec733b18a5d385daae9c3ea4caf446559044a9e97b858ecafc248c5749"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"73OBu828uoCBURcDujVXJOhQxrhiq4fEpByIAmENdlu2BrdolvoUTaP3t57XV6+iWwBmTECy5khG3b6JH4UxBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T18:51:23.208756Z","bundle_sha256":"758eb7385026fa5226242f888dbaa44ecb48805c5fa981a1b845e140a98550df"}}