{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:GA3NMCWGFDULTJM4NQ5MZBIHGD","short_pith_number":"pith:GA3NMCWG","canonical_record":{"source":{"id":"2508.00606","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-08-01T13:08:48Z","cross_cats_sorted":[],"title_canon_sha256":"4d58694ca28bef46ff7d1177c7764c02900612c1f3b4c676b9d540ae40a00cfc","abstract_canon_sha256":"776f5b92cd7dbccc16ae1d2964c71b96eca986ed29b48ce561a5937b8593b2e7"},"schema_version":"1.0"},"canonical_sha256":"3036d60ac628e8b9a59c6c3acc850730c73c877d2a92d94ede3c122d504d4173","source":{"kind":"arxiv","id":"2508.00606","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.00606","created_at":"2026-07-05T11:46:58Z"},{"alias_kind":"arxiv_version","alias_value":"2508.00606v1","created_at":"2026-07-05T11:46:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.00606","created_at":"2026-07-05T11:46:58Z"},{"alias_kind":"pith_short_12","alias_value":"GA3NMCWGFDUL","created_at":"2026-07-05T11:46:58Z"},{"alias_kind":"pith_short_16","alias_value":"GA3NMCWGFDULTJM4","created_at":"2026-07-05T11:46:58Z"},{"alias_kind":"pith_short_8","alias_value":"GA3NMCWG","created_at":"2026-07-05T11:46:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:GA3NMCWGFDULTJM4NQ5MZBIHGD","target":"record","payload":{"canonical_record":{"source":{"id":"2508.00606","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-08-01T13:08:48Z","cross_cats_sorted":[],"title_canon_sha256":"4d58694ca28bef46ff7d1177c7764c02900612c1f3b4c676b9d540ae40a00cfc","abstract_canon_sha256":"776f5b92cd7dbccc16ae1d2964c71b96eca986ed29b48ce561a5937b8593b2e7"},"schema_version":"1.0"},"canonical_sha256":"3036d60ac628e8b9a59c6c3acc850730c73c877d2a92d94ede3c122d504d4173","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:46:58.853448Z","signature_b64":"sqOJFFK1+aYnFP5RwKm0RkGVmpQRdimd9p6Xn+HE5v37Cs5Z7Nd7bgXy02SC7mnLBmn+4KEt6lXpj3iCr98HDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3036d60ac628e8b9a59c6c3acc850730c73c877d2a92d94ede3c122d504d4173","last_reissued_at":"2026-07-05T11:46:58.853007Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:46:58.853007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2508.00606","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":"2026-07-05T11:46:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tKBZOxKQUCGexRwChRQeMBaIQOx8h7nJU0nQR+heOyCEIqd7f/0+013MaeqvH3IM+VfyJDcaF5uGfOsTQF/PDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T03:16:02.620492Z"},"content_sha256":"61b5f2b43256e75a3a07afba4a108fd9f016943e92eef15a093efa518b9e5c20","schema_version":"1.0","event_id":"sha256:61b5f2b43256e75a3a07afba4a108fd9f016943e92eef15a093efa518b9e5c20"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:GA3NMCWGFDULTJM4NQ5MZBIHGD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New torsion patterns in Khovanov homology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Pedro M. G. Manch\\'on, Raquel D\\'iaz","submitted_at":"2025-08-01T13:08:48Z","abstract_excerpt":"In a previous paper by the authors, we found some patterns in link diagrams that give rise to torsion elements of order two in their Khovanov homology. In this paper we extend these results by providing new torsion patterns. Many of the torsion elements found in this way have the same homological and quantum degrees; we identify a type of submodules of the Khovanov chain complex that allows us to prove that most of these torsion elements living in the same Khovanov module are really different.\n  We use the results of this paper together with those in the previous one to find all the torsion el"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.00606","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/2508.00606/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":"2026-07-05T11:46:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XL78CHHPFQObQLLirfBWVuIL2finSNe8cNWCTNu85Ni2CXWfGKaHymKfuRUzrJY1HisUvy9znYS7TF5OPKeiCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T03:16:02.621151Z"},"content_sha256":"8c121d7d8cab907285d0b435c5d847381759da92779be50241eaee9de6728abb","schema_version":"1.0","event_id":"sha256:8c121d7d8cab907285d0b435c5d847381759da92779be50241eaee9de6728abb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GA3NMCWGFDULTJM4NQ5MZBIHGD/bundle.json","state_url":"https://pith.science/pith/GA3NMCWGFDULTJM4NQ5MZBIHGD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GA3NMCWGFDULTJM4NQ5MZBIHGD/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":"2026-08-17T03:16:02Z","links":{"resolver":"https://pith.science/pith/GA3NMCWGFDULTJM4NQ5MZBIHGD","bundle":"https://pith.science/pith/GA3NMCWGFDULTJM4NQ5MZBIHGD/bundle.json","state":"https://pith.science/pith/GA3NMCWGFDULTJM4NQ5MZBIHGD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GA3NMCWGFDULTJM4NQ5MZBIHGD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:GA3NMCWGFDULTJM4NQ5MZBIHGD","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":"776f5b92cd7dbccc16ae1d2964c71b96eca986ed29b48ce561a5937b8593b2e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-08-01T13:08:48Z","title_canon_sha256":"4d58694ca28bef46ff7d1177c7764c02900612c1f3b4c676b9d540ae40a00cfc"},"schema_version":"1.0","source":{"id":"2508.00606","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.00606","created_at":"2026-07-05T11:46:58Z"},{"alias_kind":"arxiv_version","alias_value":"2508.00606v1","created_at":"2026-07-05T11:46:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.00606","created_at":"2026-07-05T11:46:58Z"},{"alias_kind":"pith_short_12","alias_value":"GA3NMCWGFDUL","created_at":"2026-07-05T11:46:58Z"},{"alias_kind":"pith_short_16","alias_value":"GA3NMCWGFDULTJM4","created_at":"2026-07-05T11:46:58Z"},{"alias_kind":"pith_short_8","alias_value":"GA3NMCWG","created_at":"2026-07-05T11:46:58Z"}],"graph_snapshots":[{"event_id":"sha256:8c121d7d8cab907285d0b435c5d847381759da92779be50241eaee9de6728abb","target":"graph","created_at":"2026-07-05T11:46:58Z","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/2508.00606/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In a previous paper by the authors, we found some patterns in link diagrams that give rise to torsion elements of order two in their Khovanov homology. In this paper we extend these results by providing new torsion patterns. Many of the torsion elements found in this way have the same homological and quantum degrees; we identify a type of submodules of the Khovanov chain complex that allows us to prove that most of these torsion elements living in the same Khovanov module are really different.\n  We use the results of this paper together with those in the previous one to find all the torsion el","authors_text":"Pedro M. G. Manch\\'on, Raquel D\\'iaz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-08-01T13:08:48Z","title":"New torsion patterns in Khovanov homology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.00606","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":"sha256:61b5f2b43256e75a3a07afba4a108fd9f016943e92eef15a093efa518b9e5c20","target":"record","created_at":"2026-07-05T11:46:58Z","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":"776f5b92cd7dbccc16ae1d2964c71b96eca986ed29b48ce561a5937b8593b2e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-08-01T13:08:48Z","title_canon_sha256":"4d58694ca28bef46ff7d1177c7764c02900612c1f3b4c676b9d540ae40a00cfc"},"schema_version":"1.0","source":{"id":"2508.00606","kind":"arxiv","version":1}},"canonical_sha256":"3036d60ac628e8b9a59c6c3acc850730c73c877d2a92d94ede3c122d504d4173","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3036d60ac628e8b9a59c6c3acc850730c73c877d2a92d94ede3c122d504d4173","first_computed_at":"2026-07-05T11:46:58.853007Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:46:58.853007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sqOJFFK1+aYnFP5RwKm0RkGVmpQRdimd9p6Xn+HE5v37Cs5Z7Nd7bgXy02SC7mnLBmn+4KEt6lXpj3iCr98HDA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:46:58.853448Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.00606","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:61b5f2b43256e75a3a07afba4a108fd9f016943e92eef15a093efa518b9e5c20","sha256:8c121d7d8cab907285d0b435c5d847381759da92779be50241eaee9de6728abb"],"state_sha256":"675695dbee01c8f7a4c18fcad131b4d86c1838b6033c4991984515562735d35a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M8HbjMCfk9PF1z6Hg3pcY3eMeeAGe486JovhXxWEJmwTIojNpdZXfBUxphUZhZy/mWdjLp17/IYvaYRM0xdaCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T03:16:02.627495Z","bundle_sha256":"a4bad57db319e91b61205bc3e7433c63dcf2c78a637537458b4c85b375faf11e"}}