{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:RDVQ7ADMCTWALLZN5OEUNNUZMA","short_pith_number":"pith:RDVQ7ADM","canonical_record":{"source":{"id":"1701.06413","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-01-23T14:35:02Z","cross_cats_sorted":[],"title_canon_sha256":"102b377b0b339b6d63e3f31e3396a1cad27b5b093b1e1c4b0ddc211bcec416d0","abstract_canon_sha256":"7d702d0b693b42d0e8bd7e912a3700fdf27415e67955b94a80dc202a6fd90b22"},"schema_version":"1.0"},"canonical_sha256":"88eb0f806c14ec05af2deb8946b699603f0048acc1a8ec0a66334da454cfa324","source":{"kind":"arxiv","id":"1701.06413","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.06413","created_at":"2026-05-18T00:52:03Z"},{"alias_kind":"arxiv_version","alias_value":"1701.06413v2","created_at":"2026-05-18T00:52:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.06413","created_at":"2026-05-18T00:52:03Z"},{"alias_kind":"pith_short_12","alias_value":"RDVQ7ADMCTWA","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"RDVQ7ADMCTWALLZN","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"RDVQ7ADM","created_at":"2026-05-18T12:31:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:RDVQ7ADMCTWALLZN5OEUNNUZMA","target":"record","payload":{"canonical_record":{"source":{"id":"1701.06413","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-01-23T14:35:02Z","cross_cats_sorted":[],"title_canon_sha256":"102b377b0b339b6d63e3f31e3396a1cad27b5b093b1e1c4b0ddc211bcec416d0","abstract_canon_sha256":"7d702d0b693b42d0e8bd7e912a3700fdf27415e67955b94a80dc202a6fd90b22"},"schema_version":"1.0"},"canonical_sha256":"88eb0f806c14ec05af2deb8946b699603f0048acc1a8ec0a66334da454cfa324","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:03.543520Z","signature_b64":"v91SL1V/WJHKpcXicyvBBRvh+31LDIlJc0SC11L2W/JhSjHW3S4+SW2VaEmHVyus2Lj87CeBMwmQR8lp7SxOAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"88eb0f806c14ec05af2deb8946b699603f0048acc1a8ec0a66334da454cfa324","last_reissued_at":"2026-05-18T00:52:03.543019Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:03.543019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.06413","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":"2026-05-18T00:52:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Svi764eRhLvyX/Cxlf0FNQs5egyd8TWNISsoUZPhbVAjZsoHFTf9iEd2TO/8VrWqUt7MnRI6cw+ewQElZ7AADQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T07:52:56.835496Z"},"content_sha256":"edc94f4d44fc13994a0ec7ecff3657045a0c20fa19982005951d3a4d3e6c968c","schema_version":"1.0","event_id":"sha256:edc94f4d44fc13994a0ec7ecff3657045a0c20fa19982005951d3a4d3e6c968c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:RDVQ7ADMCTWALLZN5OEUNNUZMA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multifraction reduction IV: Padding and Artin-Tits groups of sufficiently large type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Derek F. Holt, Patrick Dehornoy, Sarah Rees","submitted_at":"2017-01-23T14:35:02Z","abstract_excerpt":"We investigate the padded version of reduction, an extension of multifraction reduction as defined in arXiv:1606.08991, and connect it both with ordinary reduction and with the so-called Property $\\mathrm{H}$. As an application, we show that all Artin-Tits groups of sufficiently large type satisfy some weakening Conjecture $\\mathrm{A^{padded}}$ of Conjecture $\\mathrm{A}$, thus showing that the reduction approach is relevant for these groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06413","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":"2026-05-18T00:52:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z4dfxBhypKlv+tWE5pLt9Iox6zamSmmEDwa0PtEMmj4+ZnadQx27awN22cm1YZr847EqZ5Pp8ZzW6zDCcXCiCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T07:52:56.836190Z"},"content_sha256":"02cfc786f78e91364333ea2607c1fbac54c6f0d4fa70da45e40cfc906cff6c5c","schema_version":"1.0","event_id":"sha256:02cfc786f78e91364333ea2607c1fbac54c6f0d4fa70da45e40cfc906cff6c5c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RDVQ7ADMCTWALLZN5OEUNNUZMA/bundle.json","state_url":"https://pith.science/pith/RDVQ7ADMCTWALLZN5OEUNNUZMA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RDVQ7ADMCTWALLZN5OEUNNUZMA/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":"2026-06-09T07:52:56Z","links":{"resolver":"https://pith.science/pith/RDVQ7ADMCTWALLZN5OEUNNUZMA","bundle":"https://pith.science/pith/RDVQ7ADMCTWALLZN5OEUNNUZMA/bundle.json","state":"https://pith.science/pith/RDVQ7ADMCTWALLZN5OEUNNUZMA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RDVQ7ADMCTWALLZN5OEUNNUZMA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:RDVQ7ADMCTWALLZN5OEUNNUZMA","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":"7d702d0b693b42d0e8bd7e912a3700fdf27415e67955b94a80dc202a6fd90b22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-01-23T14:35:02Z","title_canon_sha256":"102b377b0b339b6d63e3f31e3396a1cad27b5b093b1e1c4b0ddc211bcec416d0"},"schema_version":"1.0","source":{"id":"1701.06413","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.06413","created_at":"2026-05-18T00:52:03Z"},{"alias_kind":"arxiv_version","alias_value":"1701.06413v2","created_at":"2026-05-18T00:52:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.06413","created_at":"2026-05-18T00:52:03Z"},{"alias_kind":"pith_short_12","alias_value":"RDVQ7ADMCTWA","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"RDVQ7ADMCTWALLZN","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"RDVQ7ADM","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:02cfc786f78e91364333ea2607c1fbac54c6f0d4fa70da45e40cfc906cff6c5c","target":"graph","created_at":"2026-05-18T00:52:03Z","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":"We investigate the padded version of reduction, an extension of multifraction reduction as defined in arXiv:1606.08991, and connect it both with ordinary reduction and with the so-called Property $\\mathrm{H}$. As an application, we show that all Artin-Tits groups of sufficiently large type satisfy some weakening Conjecture $\\mathrm{A^{padded}}$ of Conjecture $\\mathrm{A}$, thus showing that the reduction approach is relevant for these groups.","authors_text":"Derek F. Holt, Patrick Dehornoy, Sarah Rees","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-01-23T14:35:02Z","title":"Multifraction reduction IV: Padding and Artin-Tits groups of sufficiently large type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06413","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:edc94f4d44fc13994a0ec7ecff3657045a0c20fa19982005951d3a4d3e6c968c","target":"record","created_at":"2026-05-18T00:52:03Z","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":"7d702d0b693b42d0e8bd7e912a3700fdf27415e67955b94a80dc202a6fd90b22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-01-23T14:35:02Z","title_canon_sha256":"102b377b0b339b6d63e3f31e3396a1cad27b5b093b1e1c4b0ddc211bcec416d0"},"schema_version":"1.0","source":{"id":"1701.06413","kind":"arxiv","version":2}},"canonical_sha256":"88eb0f806c14ec05af2deb8946b699603f0048acc1a8ec0a66334da454cfa324","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"88eb0f806c14ec05af2deb8946b699603f0048acc1a8ec0a66334da454cfa324","first_computed_at":"2026-05-18T00:52:03.543019Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:03.543019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v91SL1V/WJHKpcXicyvBBRvh+31LDIlJc0SC11L2W/JhSjHW3S4+SW2VaEmHVyus2Lj87CeBMwmQR8lp7SxOAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:03.543520Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.06413","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:edc94f4d44fc13994a0ec7ecff3657045a0c20fa19982005951d3a4d3e6c968c","sha256:02cfc786f78e91364333ea2607c1fbac54c6f0d4fa70da45e40cfc906cff6c5c"],"state_sha256":"a83c6782cc325fc283218abba1d065a33bf6f574c9ad1f19de49abdd0b3962c9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pXIbMMuufApBZb6oOPGQ3njqFX4pD9SbFkZYuck6BqwauRvsHh2GuoZ0avtZSaP2UGbZgzFdkq/Fu05366IhDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T07:52:56.841169Z","bundle_sha256":"16f4169306665d1c1d09a448e1cbb7b896205ee79a95145e9f8e267fc9c1704d"}}