{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:KQB7T44JCXSF6M3RVBVDW4OKRY","short_pith_number":"pith:KQB7T44J","canonical_record":{"source":{"id":"2606.21342","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2026-06-19T11:38:29Z","cross_cats_sorted":[],"title_canon_sha256":"bbd70becfe9150cd609efbf7c61157be62f3da01580125d6b3fb2775856e00ec","abstract_canon_sha256":"5bff459baca5436e6f735f83deea093accf73d235919941acce6b237c5a20171"},"schema_version":"1.0"},"canonical_sha256":"5403f9f38915e45f3371a86a3b71ca8e09163172d42d23fb1ae219b8c6999487","source":{"kind":"arxiv","id":"2606.21342","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.21342","created_at":"2026-06-23T01:12:37Z"},{"alias_kind":"arxiv_version","alias_value":"2606.21342v1","created_at":"2026-06-23T01:12:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.21342","created_at":"2026-06-23T01:12:37Z"},{"alias_kind":"pith_short_12","alias_value":"KQB7T44JCXSF","created_at":"2026-06-23T01:12:37Z"},{"alias_kind":"pith_short_16","alias_value":"KQB7T44JCXSF6M3R","created_at":"2026-06-23T01:12:37Z"},{"alias_kind":"pith_short_8","alias_value":"KQB7T44J","created_at":"2026-06-23T01:12:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:KQB7T44JCXSF6M3RVBVDW4OKRY","target":"record","payload":{"canonical_record":{"source":{"id":"2606.21342","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2026-06-19T11:38:29Z","cross_cats_sorted":[],"title_canon_sha256":"bbd70becfe9150cd609efbf7c61157be62f3da01580125d6b3fb2775856e00ec","abstract_canon_sha256":"5bff459baca5436e6f735f83deea093accf73d235919941acce6b237c5a20171"},"schema_version":"1.0"},"canonical_sha256":"5403f9f38915e45f3371a86a3b71ca8e09163172d42d23fb1ae219b8c6999487","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T01:12:37.904277Z","signature_b64":"bkXlUU3iCh7RS3WOTFKZXY1O5ENjXOUm7jrSTLPovd69+BP1hFL/SzNJrJuq++IVQ//ApMYjOymrABo91AzIAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5403f9f38915e45f3371a86a3b71ca8e09163172d42d23fb1ae219b8c6999487","last_reissued_at":"2026-06-23T01:12:37.903798Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T01:12:37.903798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.21342","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":"2026-06-23T01:12:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H2G+qA4odtqAxt6jAI4TGkqrZPkJeBYwiUAlzF2ApWMrRVni8T2kEvGMlSU4NB9KuVwh9r/sy5a/SprQS8WXCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T06:21:15.348014Z"},"content_sha256":"79cf297ba888f2f89e3d49305c88fab21d2086323077310c10fa71aa3acd8a1e","schema_version":"1.0","event_id":"sha256:79cf297ba888f2f89e3d49305c88fab21d2086323077310c10fa71aa3acd8a1e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:KQB7T44JCXSF6M3RVBVDW4OKRY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral Sequences in Semi-Abelian Categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Florent Afsa","submitted_at":"2026-06-19T11:38:29Z","abstract_excerpt":"In this paper, we define the notion of a spectral sequence in the context of semi-abelian categories in the sense of Janelidze, M\\'arki and Tholen. We show that from a double simplicial object, one can construct an exact couple, which gives rise to a spectral sequence. This extends Quillen's result on double simplicial groups to every semi-abelian category."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.21342","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/2606.21342/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":"2026-06-23T01:12:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QVClj5s0/jQuMOS4wUJcrzArxbHoiF5WhQiXsfqNTuf+TYHzgO9ssd1mf2XhU4Kh7RxTKJVCvHC8l0hCIaM1AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T06:21:15.348413Z"},"content_sha256":"b3025c36ad5aa3eeecb576b09915cc254f0bfc91822f959cf51350c7aa31cb4a","schema_version":"1.0","event_id":"sha256:b3025c36ad5aa3eeecb576b09915cc254f0bfc91822f959cf51350c7aa31cb4a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KQB7T44JCXSF6M3RVBVDW4OKRY/bundle.json","state_url":"https://pith.science/pith/KQB7T44JCXSF6M3RVBVDW4OKRY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KQB7T44JCXSF6M3RVBVDW4OKRY/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":"2026-08-14T06:21:15Z","links":{"resolver":"https://pith.science/pith/KQB7T44JCXSF6M3RVBVDW4OKRY","bundle":"https://pith.science/pith/KQB7T44JCXSF6M3RVBVDW4OKRY/bundle.json","state":"https://pith.science/pith/KQB7T44JCXSF6M3RVBVDW4OKRY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KQB7T44JCXSF6M3RVBVDW4OKRY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:KQB7T44JCXSF6M3RVBVDW4OKRY","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":"5bff459baca5436e6f735f83deea093accf73d235919941acce6b237c5a20171","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2026-06-19T11:38:29Z","title_canon_sha256":"bbd70becfe9150cd609efbf7c61157be62f3da01580125d6b3fb2775856e00ec"},"schema_version":"1.0","source":{"id":"2606.21342","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.21342","created_at":"2026-06-23T01:12:37Z"},{"alias_kind":"arxiv_version","alias_value":"2606.21342v1","created_at":"2026-06-23T01:12:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.21342","created_at":"2026-06-23T01:12:37Z"},{"alias_kind":"pith_short_12","alias_value":"KQB7T44JCXSF","created_at":"2026-06-23T01:12:37Z"},{"alias_kind":"pith_short_16","alias_value":"KQB7T44JCXSF6M3R","created_at":"2026-06-23T01:12:37Z"},{"alias_kind":"pith_short_8","alias_value":"KQB7T44J","created_at":"2026-06-23T01:12:37Z"}],"graph_snapshots":[{"event_id":"sha256:b3025c36ad5aa3eeecb576b09915cc254f0bfc91822f959cf51350c7aa31cb4a","target":"graph","created_at":"2026-06-23T01:12:37Z","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/2606.21342/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we define the notion of a spectral sequence in the context of semi-abelian categories in the sense of Janelidze, M\\'arki and Tholen. We show that from a double simplicial object, one can construct an exact couple, which gives rise to a spectral sequence. This extends Quillen's result on double simplicial groups to every semi-abelian category.","authors_text":"Florent Afsa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2026-06-19T11:38:29Z","title":"Spectral Sequences in Semi-Abelian Categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.21342","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":"sha256:79cf297ba888f2f89e3d49305c88fab21d2086323077310c10fa71aa3acd8a1e","target":"record","created_at":"2026-06-23T01:12:37Z","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":"5bff459baca5436e6f735f83deea093accf73d235919941acce6b237c5a20171","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2026-06-19T11:38:29Z","title_canon_sha256":"bbd70becfe9150cd609efbf7c61157be62f3da01580125d6b3fb2775856e00ec"},"schema_version":"1.0","source":{"id":"2606.21342","kind":"arxiv","version":1}},"canonical_sha256":"5403f9f38915e45f3371a86a3b71ca8e09163172d42d23fb1ae219b8c6999487","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5403f9f38915e45f3371a86a3b71ca8e09163172d42d23fb1ae219b8c6999487","first_computed_at":"2026-06-23T01:12:37.903798Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T01:12:37.903798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bkXlUU3iCh7RS3WOTFKZXY1O5ENjXOUm7jrSTLPovd69+BP1hFL/SzNJrJuq++IVQ//ApMYjOymrABo91AzIAA==","signature_status":"signed_v1","signed_at":"2026-06-23T01:12:37.904277Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.21342","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:79cf297ba888f2f89e3d49305c88fab21d2086323077310c10fa71aa3acd8a1e","sha256:b3025c36ad5aa3eeecb576b09915cc254f0bfc91822f959cf51350c7aa31cb4a"],"state_sha256":"d90fea34f4825fbebcaf37d1d3afa50806b932c8797902a3a4f276f454c3fb2f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/GdcU3xpWHmW1ovr6+lKcjCzaoM9YmPJZKISZb9sb+uJHMzFdW8IplJm6jbDkt8RS3FZwT2SaIeWLTVG4FDXBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T06:21:15.352020Z","bundle_sha256":"fd009a832ea67c023db59fd73741720e88401a9ed7bdfa8a8b8f63e7e44034c2"}}