{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:555ID7YCPGHOFGR2WDDRRU3NTO","short_pith_number":"pith:555ID7YC","canonical_record":{"source":{"id":"1108.5684","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-08-29T18:10:06Z","cross_cats_sorted":[],"title_canon_sha256":"da9030840a874a8321f596588fe57fd9750ac0438efac20cd466b252aa7be4bf","abstract_canon_sha256":"a4b52a73239eaae026670b62abf5d780cdfa6037c2e9fb5894314600232f7e8d"},"schema_version":"1.0"},"canonical_sha256":"ef7a81ff02798ee29a3ab0c718d36d9b868bca8c1951906713504effc9333de5","source":{"kind":"arxiv","id":"1108.5684","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.5684","created_at":"2026-05-18T04:14:36Z"},{"alias_kind":"arxiv_version","alias_value":"1108.5684v1","created_at":"2026-05-18T04:14:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.5684","created_at":"2026-05-18T04:14:36Z"},{"alias_kind":"pith_short_12","alias_value":"555ID7YCPGHO","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"555ID7YCPGHOFGR2","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"555ID7YC","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:555ID7YCPGHOFGR2WDDRRU3NTO","target":"record","payload":{"canonical_record":{"source":{"id":"1108.5684","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-08-29T18:10:06Z","cross_cats_sorted":[],"title_canon_sha256":"da9030840a874a8321f596588fe57fd9750ac0438efac20cd466b252aa7be4bf","abstract_canon_sha256":"a4b52a73239eaae026670b62abf5d780cdfa6037c2e9fb5894314600232f7e8d"},"schema_version":"1.0"},"canonical_sha256":"ef7a81ff02798ee29a3ab0c718d36d9b868bca8c1951906713504effc9333de5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:36.975694Z","signature_b64":"Hw/qazApb/u0yGQfbTBemakN/wJwaMTawR0SZAaau5rx1/B3yvlmXoWP12h2i1RZALFyYbGtkLH/EdEFkJ3OCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef7a81ff02798ee29a3ab0c718d36d9b868bca8c1951906713504effc9333de5","last_reissued_at":"2026-05-18T04:14:36.975253Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:36.975253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.5684","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":"2026-05-18T04:14:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vY9puRje5D/FZI5AHT+JvsaAXb1OTLFlW6oUinS37LDFllPg/EQKb3nDoWk6D4sDwYwgaEIL+Tnl8mwaRG6xAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T20:01:02.184526Z"},"content_sha256":"8c112a3bad64c95b9d17e995883abb01802a53973ed73cac591a3a353302e344","schema_version":"1.0","event_id":"sha256:8c112a3bad64c95b9d17e995883abb01802a53973ed73cac591a3a353302e344"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:555ID7YCPGHOFGR2WDDRRU3NTO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Snake Lemma","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Franz Lemmermeyer","submitted_at":"2011-08-29T18:10:06Z","abstract_excerpt":"We present a rather general version of the snake lemma for abelian groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5684","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":""},"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":"2026-05-18T04:14:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QXEtE9snLdMRD0kLPJWBrjrrde+WMmCY1fa2XpevFi9sNTzFuPDlrZAxcI4zE8eAo6foy4TYCxaKJeger5rHCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T20:01:02.185236Z"},"content_sha256":"4369eb680c2810982bfd5731a0a1c200b2c4f897003effe1d025528b9b3cfa0b","schema_version":"1.0","event_id":"sha256:4369eb680c2810982bfd5731a0a1c200b2c4f897003effe1d025528b9b3cfa0b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/555ID7YCPGHOFGR2WDDRRU3NTO/bundle.json","state_url":"https://pith.science/pith/555ID7YCPGHOFGR2WDDRRU3NTO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/555ID7YCPGHOFGR2WDDRRU3NTO/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":"2026-06-11T20:01:02Z","links":{"resolver":"https://pith.science/pith/555ID7YCPGHOFGR2WDDRRU3NTO","bundle":"https://pith.science/pith/555ID7YCPGHOFGR2WDDRRU3NTO/bundle.json","state":"https://pith.science/pith/555ID7YCPGHOFGR2WDDRRU3NTO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/555ID7YCPGHOFGR2WDDRRU3NTO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:555ID7YCPGHOFGR2WDDRRU3NTO","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":"a4b52a73239eaae026670b62abf5d780cdfa6037c2e9fb5894314600232f7e8d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-08-29T18:10:06Z","title_canon_sha256":"da9030840a874a8321f596588fe57fd9750ac0438efac20cd466b252aa7be4bf"},"schema_version":"1.0","source":{"id":"1108.5684","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.5684","created_at":"2026-05-18T04:14:36Z"},{"alias_kind":"arxiv_version","alias_value":"1108.5684v1","created_at":"2026-05-18T04:14:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.5684","created_at":"2026-05-18T04:14:36Z"},{"alias_kind":"pith_short_12","alias_value":"555ID7YCPGHO","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"555ID7YCPGHOFGR2","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"555ID7YC","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:4369eb680c2810982bfd5731a0a1c200b2c4f897003effe1d025528b9b3cfa0b","target":"graph","created_at":"2026-05-18T04:14:36Z","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 present a rather general version of the snake lemma for abelian groups.","authors_text":"Franz Lemmermeyer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-08-29T18:10:06Z","title":"The Snake Lemma"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5684","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":"sha256:8c112a3bad64c95b9d17e995883abb01802a53973ed73cac591a3a353302e344","target":"record","created_at":"2026-05-18T04:14:36Z","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":"a4b52a73239eaae026670b62abf5d780cdfa6037c2e9fb5894314600232f7e8d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-08-29T18:10:06Z","title_canon_sha256":"da9030840a874a8321f596588fe57fd9750ac0438efac20cd466b252aa7be4bf"},"schema_version":"1.0","source":{"id":"1108.5684","kind":"arxiv","version":1}},"canonical_sha256":"ef7a81ff02798ee29a3ab0c718d36d9b868bca8c1951906713504effc9333de5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ef7a81ff02798ee29a3ab0c718d36d9b868bca8c1951906713504effc9333de5","first_computed_at":"2026-05-18T04:14:36.975253Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:36.975253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Hw/qazApb/u0yGQfbTBemakN/wJwaMTawR0SZAaau5rx1/B3yvlmXoWP12h2i1RZALFyYbGtkLH/EdEFkJ3OCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:36.975694Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.5684","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c112a3bad64c95b9d17e995883abb01802a53973ed73cac591a3a353302e344","sha256:4369eb680c2810982bfd5731a0a1c200b2c4f897003effe1d025528b9b3cfa0b"],"state_sha256":"8fc7488e42e6d7f1ef9c4b341c5507c06984dd96850b7eca3d9892fbabe30356"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sJRs4+i4y9d71mtVLp8acYFbupQglBdJXFB3QPAkqLngRmMQjw+AZJy1EAGsu4/BIFhUpaR2EiacSx7ZckwTDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T20:01:02.189920Z","bundle_sha256":"b8f729b240c65ddb9c8dd9bbf73cf3d3b9d41efda2ad491e22e9159cc19b0512"}}