{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ARJG3BREZUZRVI4GD2I2JBG63N","short_pith_number":"pith:ARJG3BRE","canonical_record":{"source":{"id":"1809.00499","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-09-03T08:42:25Z","cross_cats_sorted":["math.CT","math.QA"],"title_canon_sha256":"2be5ed2d87d70bdf5172eeb6de2dce6bc9ba1275de77a06afa37e314bd767333","abstract_canon_sha256":"4ff1f63846aa2b6599402dc1ff1f2a5914cb2a207012937f295fce7116a86f46"},"schema_version":"1.0"},"canonical_sha256":"04526d8624cd331aa3861e91a484dedb7be1cad50c993bd7bf160f3c3ef7beb9","source":{"kind":"arxiv","id":"1809.00499","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.00499","created_at":"2026-07-05T02:21:11Z"},{"alias_kind":"arxiv_version","alias_value":"1809.00499v2","created_at":"2026-07-05T02:21:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.00499","created_at":"2026-07-05T02:21:11Z"},{"alias_kind":"pith_short_12","alias_value":"ARJG3BREZUZR","created_at":"2026-07-05T02:21:11Z"},{"alias_kind":"pith_short_16","alias_value":"ARJG3BREZUZRVI4G","created_at":"2026-07-05T02:21:11Z"},{"alias_kind":"pith_short_8","alias_value":"ARJG3BRE","created_at":"2026-07-05T02:21:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ARJG3BREZUZRVI4GD2I2JBG63N","target":"record","payload":{"canonical_record":{"source":{"id":"1809.00499","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-09-03T08:42:25Z","cross_cats_sorted":["math.CT","math.QA"],"title_canon_sha256":"2be5ed2d87d70bdf5172eeb6de2dce6bc9ba1275de77a06afa37e314bd767333","abstract_canon_sha256":"4ff1f63846aa2b6599402dc1ff1f2a5914cb2a207012937f295fce7116a86f46"},"schema_version":"1.0"},"canonical_sha256":"04526d8624cd331aa3861e91a484dedb7be1cad50c993bd7bf160f3c3ef7beb9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:21:11.890908Z","signature_b64":"ANwospUKRN0biMY/49Z3QWIeuCHV5oS/bTFxmgQ1ndsWqarI8edt6sjb0FsNWlz55Roj3o38tUZ2NhGD1WLIDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"04526d8624cd331aa3861e91a484dedb7be1cad50c993bd7bf160f3c3ef7beb9","last_reissued_at":"2026-07-05T02:21:11.890518Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:21:11.890518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.00499","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":"2026-07-05T02:21:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lPDsSkPHepGPjmI8/2bFQyVn1jMFLPNYSX+iHpHXjKDMnbB9xyUQtRzOgzavDFJcPo/z0V97kixBo2EOkYuiBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T23:47:04.482167Z"},"content_sha256":"9aae9546e2aebbfc92015502397ed48b075e41281a4ed20c31e0abb0e5907c02","schema_version":"1.0","event_id":"sha256:9aae9546e2aebbfc92015502397ed48b075e41281a4ed20c31e0abb0e5907c02"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ARJG3BREZUZRVI4GD2I2JBG63N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"M-traces in (non-unimodular) pivotal categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.QA"],"primary_cat":"math.RT","authors_text":"Bertrand Patureau-Mirand, Jonathan Kujawa, Nathan Geer","submitted_at":"2018-09-03T08:42:25Z","abstract_excerpt":"We generalize the notion of a modified trace (or m-trace) to the setting of non-unimodular categories. M-traces are known to play an important role in low-dimensional topology and representation theory, as well as in studying the category itself. Under mild conditions we give existence and uniqueness results for m-traces in pivotal categories."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.00499","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1809.00499/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":"2026-07-05T02:21:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jnOWI8T2Jcx+f8qyN33FY8WF5mOEdICSJLObAb5QbQMx9tg2J3WqUkG4jI4RiGRfMm+EN7ZDjnpNVKKusygnBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T23:47:04.483049Z"},"content_sha256":"3b823d606121620a3a9601ebe9110e51848b9eeec501b2ab54a82aa09cbc2767","schema_version":"1.0","event_id":"sha256:3b823d606121620a3a9601ebe9110e51848b9eeec501b2ab54a82aa09cbc2767"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ARJG3BREZUZRVI4GD2I2JBG63N/bundle.json","state_url":"https://pith.science/pith/ARJG3BREZUZRVI4GD2I2JBG63N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ARJG3BREZUZRVI4GD2I2JBG63N/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":"2026-08-12T23:47:04Z","links":{"resolver":"https://pith.science/pith/ARJG3BREZUZRVI4GD2I2JBG63N","bundle":"https://pith.science/pith/ARJG3BREZUZRVI4GD2I2JBG63N/bundle.json","state":"https://pith.science/pith/ARJG3BREZUZRVI4GD2I2JBG63N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ARJG3BREZUZRVI4GD2I2JBG63N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ARJG3BREZUZRVI4GD2I2JBG63N","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":"4ff1f63846aa2b6599402dc1ff1f2a5914cb2a207012937f295fce7116a86f46","cross_cats_sorted":["math.CT","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-09-03T08:42:25Z","title_canon_sha256":"2be5ed2d87d70bdf5172eeb6de2dce6bc9ba1275de77a06afa37e314bd767333"},"schema_version":"1.0","source":{"id":"1809.00499","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.00499","created_at":"2026-07-05T02:21:11Z"},{"alias_kind":"arxiv_version","alias_value":"1809.00499v2","created_at":"2026-07-05T02:21:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.00499","created_at":"2026-07-05T02:21:11Z"},{"alias_kind":"pith_short_12","alias_value":"ARJG3BREZUZR","created_at":"2026-07-05T02:21:11Z"},{"alias_kind":"pith_short_16","alias_value":"ARJG3BREZUZRVI4G","created_at":"2026-07-05T02:21:11Z"},{"alias_kind":"pith_short_8","alias_value":"ARJG3BRE","created_at":"2026-07-05T02:21:11Z"}],"graph_snapshots":[{"event_id":"sha256:3b823d606121620a3a9601ebe9110e51848b9eeec501b2ab54a82aa09cbc2767","target":"graph","created_at":"2026-07-05T02:21:11Z","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/1809.00499/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We generalize the notion of a modified trace (or m-trace) to the setting of non-unimodular categories. M-traces are known to play an important role in low-dimensional topology and representation theory, as well as in studying the category itself. Under mild conditions we give existence and uniqueness results for m-traces in pivotal categories.","authors_text":"Bertrand Patureau-Mirand, Jonathan Kujawa, Nathan Geer","cross_cats":["math.CT","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-09-03T08:42:25Z","title":"M-traces in (non-unimodular) pivotal categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.00499","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":"sha256:9aae9546e2aebbfc92015502397ed48b075e41281a4ed20c31e0abb0e5907c02","target":"record","created_at":"2026-07-05T02:21:11Z","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":"4ff1f63846aa2b6599402dc1ff1f2a5914cb2a207012937f295fce7116a86f46","cross_cats_sorted":["math.CT","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-09-03T08:42:25Z","title_canon_sha256":"2be5ed2d87d70bdf5172eeb6de2dce6bc9ba1275de77a06afa37e314bd767333"},"schema_version":"1.0","source":{"id":"1809.00499","kind":"arxiv","version":2}},"canonical_sha256":"04526d8624cd331aa3861e91a484dedb7be1cad50c993bd7bf160f3c3ef7beb9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"04526d8624cd331aa3861e91a484dedb7be1cad50c993bd7bf160f3c3ef7beb9","first_computed_at":"2026-07-05T02:21:11.890518Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:21:11.890518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ANwospUKRN0biMY/49Z3QWIeuCHV5oS/bTFxmgQ1ndsWqarI8edt6sjb0FsNWlz55Roj3o38tUZ2NhGD1WLIDw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:21:11.890908Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.00499","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9aae9546e2aebbfc92015502397ed48b075e41281a4ed20c31e0abb0e5907c02","sha256:3b823d606121620a3a9601ebe9110e51848b9eeec501b2ab54a82aa09cbc2767"],"state_sha256":"1bed5c0bc8ef9045250974d36b0a9152e27088f158028c6b19a0037aadebde47"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4CZgS+9gP5WudtbBcBccGAgK+zOdyli7XNWiXAKkfuhWEfG1QQqv6zPb7tArz92GQdOwPVvdj9/5t6gIia1XAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T23:47:04.519266Z","bundle_sha256":"da9faa1c2aada1a10f23346cc3c27eabbc1d08fdc7cb2c02140943891819fb79"}}