{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:ZMRNDLDGGVSXL4H53RXIG5B43X","short_pith_number":"pith:ZMRNDLDG","canonical_record":{"source":{"id":"1712.04181","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-12-12T09:06:41Z","cross_cats_sorted":["math.DS","math.NT"],"title_canon_sha256":"fa9a47c1e3267c364b92532baad81a049812041f08b2e0f4131845e1583c8c02","abstract_canon_sha256":"4b6a1f4e0341b7ab3d41db965d0d96c68ebfc171a098a98c8ab79d92651008b1"},"schema_version":"1.0"},"canonical_sha256":"cb22d1ac66356575f0fddc6e83743cddc1ba7b855614d96e6eda34e42c08af9c","source":{"kind":"arxiv","id":"1712.04181","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.04181","created_at":"2026-05-18T00:19:56Z"},{"alias_kind":"arxiv_version","alias_value":"1712.04181v2","created_at":"2026-05-18T00:19:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.04181","created_at":"2026-05-18T00:19:56Z"},{"alias_kind":"pith_short_12","alias_value":"ZMRNDLDGGVSX","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZMRNDLDGGVSXL4H5","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZMRNDLDG","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:ZMRNDLDGGVSXL4H53RXIG5B43X","target":"record","payload":{"canonical_record":{"source":{"id":"1712.04181","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-12-12T09:06:41Z","cross_cats_sorted":["math.DS","math.NT"],"title_canon_sha256":"fa9a47c1e3267c364b92532baad81a049812041f08b2e0f4131845e1583c8c02","abstract_canon_sha256":"4b6a1f4e0341b7ab3d41db965d0d96c68ebfc171a098a98c8ab79d92651008b1"},"schema_version":"1.0"},"canonical_sha256":"cb22d1ac66356575f0fddc6e83743cddc1ba7b855614d96e6eda34e42c08af9c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:56.633412Z","signature_b64":"rlnhI/fa3lOjSwsFDL/GAkmfORZYNT+fAdjwJnk/dHuDNutuSMg5/qN8uoh3mTclskJylO0zHdWrecSnLCMnAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb22d1ac66356575f0fddc6e83743cddc1ba7b855614d96e6eda34e42c08af9c","last_reissued_at":"2026-05-18T00:19:56.632681Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:56.632681Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.04181","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":"2026-05-18T00:19:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L0Gm8CyiqNqDVOi/uDBb4JBeS0Y7WmeM/xAuC98cBC0h1z44kFLS9pd+a4EIKONp2Z2EwoYMbAJiwIMjBA52Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T07:17:04.067047Z"},"content_sha256":"50bdf94d2bec07e136dd6e4e49a6c7497b5394a1e0667b2f57d237e5bd15775d","schema_version":"1.0","event_id":"sha256:50bdf94d2bec07e136dd6e4e49a6c7497b5394a1e0667b2f57d237e5bd15775d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:ZMRNDLDGGVSXL4H53RXIG5B43X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the leafwise cohomology and dynamical zeta functions for fiber bundles over the circle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.NT"],"primary_cat":"math.DG","authors_text":"Junhyeong Kim","submitted_at":"2017-12-12T09:06:41Z","abstract_excerpt":"In this paper, we give concrete descriptions of leafwise cohomology groups and show the regularized determinant expression of the dynamical zeta function for fiber bundles over $S^{1}$. As applications, we show a functional equation and some formulas for special values of the dynamical zeta function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.04181","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":""},"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":"2026-05-18T00:19:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kyNGQxaFMAcJ9DtjkBGnL6BdKGLKpQaUSADW847mZrINc3v2hzplF6Io/OL/PW1C68KiY0mhG6fjrqxnHc7oAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T07:17:04.067403Z"},"content_sha256":"b7af58afb65d6f57f10edd44084579a559560783282e927c6478207cf8d67491","schema_version":"1.0","event_id":"sha256:b7af58afb65d6f57f10edd44084579a559560783282e927c6478207cf8d67491"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZMRNDLDGGVSXL4H53RXIG5B43X/bundle.json","state_url":"https://pith.science/pith/ZMRNDLDGGVSXL4H53RXIG5B43X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZMRNDLDGGVSXL4H53RXIG5B43X/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":"2026-06-02T07:17:04Z","links":{"resolver":"https://pith.science/pith/ZMRNDLDGGVSXL4H53RXIG5B43X","bundle":"https://pith.science/pith/ZMRNDLDGGVSXL4H53RXIG5B43X/bundle.json","state":"https://pith.science/pith/ZMRNDLDGGVSXL4H53RXIG5B43X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZMRNDLDGGVSXL4H53RXIG5B43X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZMRNDLDGGVSXL4H53RXIG5B43X","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":"4b6a1f4e0341b7ab3d41db965d0d96c68ebfc171a098a98c8ab79d92651008b1","cross_cats_sorted":["math.DS","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-12-12T09:06:41Z","title_canon_sha256":"fa9a47c1e3267c364b92532baad81a049812041f08b2e0f4131845e1583c8c02"},"schema_version":"1.0","source":{"id":"1712.04181","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.04181","created_at":"2026-05-18T00:19:56Z"},{"alias_kind":"arxiv_version","alias_value":"1712.04181v2","created_at":"2026-05-18T00:19:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.04181","created_at":"2026-05-18T00:19:56Z"},{"alias_kind":"pith_short_12","alias_value":"ZMRNDLDGGVSX","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZMRNDLDGGVSXL4H5","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZMRNDLDG","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:b7af58afb65d6f57f10edd44084579a559560783282e927c6478207cf8d67491","target":"graph","created_at":"2026-05-18T00:19:56Z","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":"In this paper, we give concrete descriptions of leafwise cohomology groups and show the regularized determinant expression of the dynamical zeta function for fiber bundles over $S^{1}$. As applications, we show a functional equation and some formulas for special values of the dynamical zeta function.","authors_text":"Junhyeong Kim","cross_cats":["math.DS","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-12-12T09:06:41Z","title":"On the leafwise cohomology and dynamical zeta functions for fiber bundles over the circle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.04181","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":"sha256:50bdf94d2bec07e136dd6e4e49a6c7497b5394a1e0667b2f57d237e5bd15775d","target":"record","created_at":"2026-05-18T00:19:56Z","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":"4b6a1f4e0341b7ab3d41db965d0d96c68ebfc171a098a98c8ab79d92651008b1","cross_cats_sorted":["math.DS","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-12-12T09:06:41Z","title_canon_sha256":"fa9a47c1e3267c364b92532baad81a049812041f08b2e0f4131845e1583c8c02"},"schema_version":"1.0","source":{"id":"1712.04181","kind":"arxiv","version":2}},"canonical_sha256":"cb22d1ac66356575f0fddc6e83743cddc1ba7b855614d96e6eda34e42c08af9c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb22d1ac66356575f0fddc6e83743cddc1ba7b855614d96e6eda34e42c08af9c","first_computed_at":"2026-05-18T00:19:56.632681Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:56.632681Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rlnhI/fa3lOjSwsFDL/GAkmfORZYNT+fAdjwJnk/dHuDNutuSMg5/qN8uoh3mTclskJylO0zHdWrecSnLCMnAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:56.633412Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.04181","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50bdf94d2bec07e136dd6e4e49a6c7497b5394a1e0667b2f57d237e5bd15775d","sha256:b7af58afb65d6f57f10edd44084579a559560783282e927c6478207cf8d67491"],"state_sha256":"d6eb7aad67bcc1c48e6e5e68e366bec9e5d3330756407c9093e5bdb804662b1a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kcslJ7wO0Rw7DSaKhDM2TQkj8bu60N5R/yMPSoVAuFXGFFNpTE8GWafva9fivuYzqwkuy7e+mLsXccdCt8lmAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T07:17:04.069325Z","bundle_sha256":"612ed225c530e9f818a0d37ec585276edbfd95c0ae588696460b0452d5f836ea"}}