{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:F2EURGHKZ4KTW2HKXAYWYNSEVZ","short_pith_number":"pith:F2EURGHK","canonical_record":{"source":{"id":"1807.07786","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-07-20T10:52:16Z","cross_cats_sorted":[],"title_canon_sha256":"d1b782141fb6fff1b8fbc80bc50307853d1e2e05e1d899f92eb5e15bb45fd70a","abstract_canon_sha256":"23e83b8188257df25acfc1643f4e5a06006cb61374c1e0dac03bd19b6cf6f52f"},"schema_version":"1.0"},"canonical_sha256":"2e894898eacf153b68eab8316c3644ae7fcef30cb570b3ca7a5a3f9cb366d0d6","source":{"kind":"arxiv","id":"1807.07786","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.07786","created_at":"2026-07-05T04:00:10Z"},{"alias_kind":"arxiv_version","alias_value":"1807.07786v5","created_at":"2026-07-05T04:00:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.07786","created_at":"2026-07-05T04:00:10Z"},{"alias_kind":"pith_short_12","alias_value":"F2EURGHKZ4KT","created_at":"2026-07-05T04:00:10Z"},{"alias_kind":"pith_short_16","alias_value":"F2EURGHKZ4KTW2HK","created_at":"2026-07-05T04:00:10Z"},{"alias_kind":"pith_short_8","alias_value":"F2EURGHK","created_at":"2026-07-05T04:00:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:F2EURGHKZ4KTW2HKXAYWYNSEVZ","target":"record","payload":{"canonical_record":{"source":{"id":"1807.07786","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-07-20T10:52:16Z","cross_cats_sorted":[],"title_canon_sha256":"d1b782141fb6fff1b8fbc80bc50307853d1e2e05e1d899f92eb5e15bb45fd70a","abstract_canon_sha256":"23e83b8188257df25acfc1643f4e5a06006cb61374c1e0dac03bd19b6cf6f52f"},"schema_version":"1.0"},"canonical_sha256":"2e894898eacf153b68eab8316c3644ae7fcef30cb570b3ca7a5a3f9cb366d0d6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:00:10.083387Z","signature_b64":"i1oTvupA+KikhYs/J9ynF/eE3+0pnd4wcNhTl+vB+AgM+eZAKfUGUxuGNWPpvahiXDjQYFzMjzskNN8hLOQMDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e894898eacf153b68eab8316c3644ae7fcef30cb570b3ca7a5a3f9cb366d0d6","last_reissued_at":"2026-07-05T04:00:10.082796Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:00:10.082796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.07786","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:00:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1VJP/fbTZhjMqgoYkAjHXR0thLWBEfw3a6LeU+aAfvAmAv/Av7Qosss6uJXUyhDKfqjydQDXtkAIMq43o1jADw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T08:46:08.749465Z"},"content_sha256":"9b2260a6bc871dce429a821816c384ba6d63d554060450bc398fba270769a9c9","schema_version":"1.0","event_id":"sha256:9b2260a6bc871dce429a821816c384ba6d63d554060450bc398fba270769a9c9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:F2EURGHKZ4KTW2HKXAYWYNSEVZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Betti side of the double shuffle theory. II. Double shuffle relations for associators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Benjamin Enriquez, Hidekazu Furusho","submitted_at":"2018-07-20T10:52:16Z","abstract_excerpt":"We derive from the compatibility of associators with the module harmonic coproduct, obtained in Part I of the series, the inclusion of the torsor of associators into that of double shuffle relations, which completes one of the aims of this series. We define two stabilizer torsors using the module and algebra harmonic coproducts from Part I. We show that the double shuffle torsor can be described using the module stabilizer torsor, and that the latter torsor is contained in the algebra stabilizer torsor."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.07786","kind":"arxiv","version":5},"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/1807.07786/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":"2026-07-05T04:00:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YjMT15eOnn1Ldcd8TwMKfDkhhHjXcOPpv5sOqMwO4Jen0VljpvEePRSXXcxxqLxkvYEf6vQUNLNTMM7XEMGfDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T08:46:08.749997Z"},"content_sha256":"40d0661b6c76e03140b2d2c5f97cd8d45ad09c00f096bf892564304969a0a336","schema_version":"1.0","event_id":"sha256:40d0661b6c76e03140b2d2c5f97cd8d45ad09c00f096bf892564304969a0a336"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F2EURGHKZ4KTW2HKXAYWYNSEVZ/bundle.json","state_url":"https://pith.science/pith/F2EURGHKZ4KTW2HKXAYWYNSEVZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F2EURGHKZ4KTW2HKXAYWYNSEVZ/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":"2026-08-17T08:46:08Z","links":{"resolver":"https://pith.science/pith/F2EURGHKZ4KTW2HKXAYWYNSEVZ","bundle":"https://pith.science/pith/F2EURGHKZ4KTW2HKXAYWYNSEVZ/bundle.json","state":"https://pith.science/pith/F2EURGHKZ4KTW2HKXAYWYNSEVZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F2EURGHKZ4KTW2HKXAYWYNSEVZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:F2EURGHKZ4KTW2HKXAYWYNSEVZ","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":"23e83b8188257df25acfc1643f4e5a06006cb61374c1e0dac03bd19b6cf6f52f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-07-20T10:52:16Z","title_canon_sha256":"d1b782141fb6fff1b8fbc80bc50307853d1e2e05e1d899f92eb5e15bb45fd70a"},"schema_version":"1.0","source":{"id":"1807.07786","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.07786","created_at":"2026-07-05T04:00:10Z"},{"alias_kind":"arxiv_version","alias_value":"1807.07786v5","created_at":"2026-07-05T04:00:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.07786","created_at":"2026-07-05T04:00:10Z"},{"alias_kind":"pith_short_12","alias_value":"F2EURGHKZ4KT","created_at":"2026-07-05T04:00:10Z"},{"alias_kind":"pith_short_16","alias_value":"F2EURGHKZ4KTW2HK","created_at":"2026-07-05T04:00:10Z"},{"alias_kind":"pith_short_8","alias_value":"F2EURGHK","created_at":"2026-07-05T04:00:10Z"}],"graph_snapshots":[{"event_id":"sha256:40d0661b6c76e03140b2d2c5f97cd8d45ad09c00f096bf892564304969a0a336","target":"graph","created_at":"2026-07-05T04:00:10Z","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/1807.07786/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We derive from the compatibility of associators with the module harmonic coproduct, obtained in Part I of the series, the inclusion of the torsor of associators into that of double shuffle relations, which completes one of the aims of this series. We define two stabilizer torsors using the module and algebra harmonic coproducts from Part I. We show that the double shuffle torsor can be described using the module stabilizer torsor, and that the latter torsor is contained in the algebra stabilizer torsor.","authors_text":"Benjamin Enriquez, Hidekazu Furusho","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-07-20T10:52:16Z","title":"The Betti side of the double shuffle theory. II. Double shuffle relations for associators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.07786","kind":"arxiv","version":5},"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":"sha256:9b2260a6bc871dce429a821816c384ba6d63d554060450bc398fba270769a9c9","target":"record","created_at":"2026-07-05T04:00:10Z","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":"23e83b8188257df25acfc1643f4e5a06006cb61374c1e0dac03bd19b6cf6f52f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-07-20T10:52:16Z","title_canon_sha256":"d1b782141fb6fff1b8fbc80bc50307853d1e2e05e1d899f92eb5e15bb45fd70a"},"schema_version":"1.0","source":{"id":"1807.07786","kind":"arxiv","version":5}},"canonical_sha256":"2e894898eacf153b68eab8316c3644ae7fcef30cb570b3ca7a5a3f9cb366d0d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2e894898eacf153b68eab8316c3644ae7fcef30cb570b3ca7a5a3f9cb366d0d6","first_computed_at":"2026-07-05T04:00:10.082796Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:00:10.082796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i1oTvupA+KikhYs/J9ynF/eE3+0pnd4wcNhTl+vB+AgM+eZAKfUGUxuGNWPpvahiXDjQYFzMjzskNN8hLOQMDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:00:10.083387Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.07786","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b2260a6bc871dce429a821816c384ba6d63d554060450bc398fba270769a9c9","sha256:40d0661b6c76e03140b2d2c5f97cd8d45ad09c00f096bf892564304969a0a336"],"state_sha256":"440c5abe1750327ca85224088a74ac8f5ce5cf7509d7f49cd60a6d9c95a7861a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"raSz8e5WYNIrdgkMgce8QDDYJvs/8BheSds21BnPGj4pKRqiR0d5cwpPDesycHZ8hnUj9NmEqfklC6RLBbhtCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T08:46:08.754549Z","bundle_sha256":"9e19fcc2c1224959fa849e01517df51e70ea8c127336a66c17c55c5da5df2a76"}}