{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:NJDZF6UFQPGACUNUAHVSXQWZIA","short_pith_number":"pith:NJDZF6UF","canonical_record":{"source":{"id":"1003.4902","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-03-25T14:15:29Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"85399bf0ce6cf863ad6cf56efe8d4a611216e62672e12cfc27b7def0bc2c2b62","abstract_canon_sha256":"c3046b0cc4d8df9ea7225fb63851ac9aa0417f06ca18f1352a4f4748dd70c553"},"schema_version":"1.0"},"canonical_sha256":"6a4792fa8583cc0151b401eb2bc2d94021be98a8ddf403400dfefdfec9e3ade3","source":{"kind":"arxiv","id":"1003.4902","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.4902","created_at":"2026-05-18T02:08:23Z"},{"alias_kind":"arxiv_version","alias_value":"1003.4902v1","created_at":"2026-05-18T02:08:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.4902","created_at":"2026-05-18T02:08:23Z"},{"alias_kind":"pith_short_12","alias_value":"NJDZF6UFQPGA","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"NJDZF6UFQPGACUNU","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"NJDZF6UF","created_at":"2026-05-18T12:26:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:NJDZF6UFQPGACUNUAHVSXQWZIA","target":"record","payload":{"canonical_record":{"source":{"id":"1003.4902","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-03-25T14:15:29Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"85399bf0ce6cf863ad6cf56efe8d4a611216e62672e12cfc27b7def0bc2c2b62","abstract_canon_sha256":"c3046b0cc4d8df9ea7225fb63851ac9aa0417f06ca18f1352a4f4748dd70c553"},"schema_version":"1.0"},"canonical_sha256":"6a4792fa8583cc0151b401eb2bc2d94021be98a8ddf403400dfefdfec9e3ade3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:08:23.023290Z","signature_b64":"ZaGo/75TcloEwnrI/bXmDSW96nH4bTcNrzyaCX9dc40npt+ih2oIOiryfGXnK1aa0R7/Bi3vdadLvXbafuzJDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a4792fa8583cc0151b401eb2bc2d94021be98a8ddf403400dfefdfec9e3ade3","last_reissued_at":"2026-05-18T02:08:23.022461Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:08:23.022461Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1003.4902","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":"2026-05-18T02:08:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZlM9Fh8wNE/SQf8r9+1zELlHl+EyCmwCsaenBE0mUkj2bVyFNRLeXe3y5a4mu4fUUrPkoud6aDZuaeqowhTsDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T01:59:33.665894Z"},"content_sha256":"c299bad86340d30bbcb21d2e0855dcf0a43ccb745d9b46279162734cd7573533","schema_version":"1.0","event_id":"sha256:c299bad86340d30bbcb21d2e0855dcf0a43ccb745d9b46279162734cd7573533"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:NJDZF6UFQPGACUNUAHVSXQWZIA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Zeta-functions of renormalizable sub-Lorenz templates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.GT","authors_text":"Luis Silva, Nuno Franco","submitted_at":"2010-03-25T14:15:29Z","abstract_excerpt":"We describe the Williams zeta functions and the twist zeta functions of sub-Lorenz templates generated by renormalizable Lorenz maps, in terms of the corresponding zeta-functions of the sub-Lorenz templates generated by the renormalized map and by the  map that determines the renormalization type."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.4902","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":"2026-05-18T02:08:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kBGJ8573VFJDSlK9dj7VtOCdLMCyxqKGP6Z2sDLPnb/mkDAcwUnBLFbWEft+tM5Xvb77t16OAlRbQ3qV7v85DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T01:59:33.666237Z"},"content_sha256":"ce2ac179cd11d53610350a1810273bd245933c3b6825e82d22cf9196e485a126","schema_version":"1.0","event_id":"sha256:ce2ac179cd11d53610350a1810273bd245933c3b6825e82d22cf9196e485a126"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NJDZF6UFQPGACUNUAHVSXQWZIA/bundle.json","state_url":"https://pith.science/pith/NJDZF6UFQPGACUNUAHVSXQWZIA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NJDZF6UFQPGACUNUAHVSXQWZIA/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":"2026-06-26T01:59:33Z","links":{"resolver":"https://pith.science/pith/NJDZF6UFQPGACUNUAHVSXQWZIA","bundle":"https://pith.science/pith/NJDZF6UFQPGACUNUAHVSXQWZIA/bundle.json","state":"https://pith.science/pith/NJDZF6UFQPGACUNUAHVSXQWZIA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NJDZF6UFQPGACUNUAHVSXQWZIA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:NJDZF6UFQPGACUNUAHVSXQWZIA","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":"c3046b0cc4d8df9ea7225fb63851ac9aa0417f06ca18f1352a4f4748dd70c553","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-03-25T14:15:29Z","title_canon_sha256":"85399bf0ce6cf863ad6cf56efe8d4a611216e62672e12cfc27b7def0bc2c2b62"},"schema_version":"1.0","source":{"id":"1003.4902","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.4902","created_at":"2026-05-18T02:08:23Z"},{"alias_kind":"arxiv_version","alias_value":"1003.4902v1","created_at":"2026-05-18T02:08:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.4902","created_at":"2026-05-18T02:08:23Z"},{"alias_kind":"pith_short_12","alias_value":"NJDZF6UFQPGA","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"NJDZF6UFQPGACUNU","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"NJDZF6UF","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:ce2ac179cd11d53610350a1810273bd245933c3b6825e82d22cf9196e485a126","target":"graph","created_at":"2026-05-18T02:08:23Z","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 describe the Williams zeta functions and the twist zeta functions of sub-Lorenz templates generated by renormalizable Lorenz maps, in terms of the corresponding zeta-functions of the sub-Lorenz templates generated by the renormalized map and by the  map that determines the renormalization type.","authors_text":"Luis Silva, Nuno Franco","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-03-25T14:15:29Z","title":"Zeta-functions of renormalizable sub-Lorenz templates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.4902","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:c299bad86340d30bbcb21d2e0855dcf0a43ccb745d9b46279162734cd7573533","target":"record","created_at":"2026-05-18T02:08:23Z","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":"c3046b0cc4d8df9ea7225fb63851ac9aa0417f06ca18f1352a4f4748dd70c553","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-03-25T14:15:29Z","title_canon_sha256":"85399bf0ce6cf863ad6cf56efe8d4a611216e62672e12cfc27b7def0bc2c2b62"},"schema_version":"1.0","source":{"id":"1003.4902","kind":"arxiv","version":1}},"canonical_sha256":"6a4792fa8583cc0151b401eb2bc2d94021be98a8ddf403400dfefdfec9e3ade3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a4792fa8583cc0151b401eb2bc2d94021be98a8ddf403400dfefdfec9e3ade3","first_computed_at":"2026-05-18T02:08:23.022461Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:08:23.022461Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZaGo/75TcloEwnrI/bXmDSW96nH4bTcNrzyaCX9dc40npt+ih2oIOiryfGXnK1aa0R7/Bi3vdadLvXbafuzJDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:08:23.023290Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.4902","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c299bad86340d30bbcb21d2e0855dcf0a43ccb745d9b46279162734cd7573533","sha256:ce2ac179cd11d53610350a1810273bd245933c3b6825e82d22cf9196e485a126"],"state_sha256":"a202ce3ca32acccffb6ac91cafac04355a14e9fb6c06028146cf88a5a11b72e8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8kAiK8rmKoBGvB+UZmBnYSu+6VGogRhhfQ8Ve35NOD9EVr3dtAl3gAhSw9urNfZrFGnyAH/ME06uP4DxW2QgDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T01:59:33.668154Z","bundle_sha256":"6cea0af1a21a455eb3dbc5e684552a4d7149645766f1901f3ee34d0306d5706b"}}