{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2000:XCR7CWPMXDBSUWS64TGSGTO35B","short_pith_number":"pith:XCR7CWPM","canonical_record":{"source":{"id":"math/0004141","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AT","submitted_at":"2000-04-23T17:27:44Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"3a5a25cd19729643f3e31aa920a313c689af315c707aa80f35beb2556b5bd502","abstract_canon_sha256":"d8bfbfa717c55783eac5a78b9ee99921a8f3905e9cb538b8d6c8b9f7be816b2b"},"schema_version":"1.0"},"canonical_sha256":"b8a3f159ecb8c32a5a5ee4cd234ddbe86c24dd8afe36ba140982191852a44877","source":{"kind":"arxiv","id":"math/0004141","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0004141","created_at":"2026-05-18T03:54:26Z"},{"alias_kind":"arxiv_version","alias_value":"math/0004141v1","created_at":"2026-05-18T03:54:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0004141","created_at":"2026-05-18T03:54:26Z"},{"alias_kind":"pith_short_12","alias_value":"XCR7CWPMXDBS","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"XCR7CWPMXDBSUWS6","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"XCR7CWPM","created_at":"2026-05-18T12:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2000:XCR7CWPMXDBSUWS64TGSGTO35B","target":"record","payload":{"canonical_record":{"source":{"id":"math/0004141","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AT","submitted_at":"2000-04-23T17:27:44Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"3a5a25cd19729643f3e31aa920a313c689af315c707aa80f35beb2556b5bd502","abstract_canon_sha256":"d8bfbfa717c55783eac5a78b9ee99921a8f3905e9cb538b8d6c8b9f7be816b2b"},"schema_version":"1.0"},"canonical_sha256":"b8a3f159ecb8c32a5a5ee4cd234ddbe86c24dd8afe36ba140982191852a44877","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:26.574741Z","signature_b64":"GP27vcQqSdMrhztFvvFwRWDlJJEBBU02m0HmMKddqWQaj7fiIAP+BXcsUNLmQEQ2AHn6wet7xYJAwtH+TD2kBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b8a3f159ecb8c32a5a5ee4cd234ddbe86c24dd8afe36ba140982191852a44877","last_reissued_at":"2026-05-18T03:54:26.574015Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:26.574015Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0004141","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":"2026-05-18T03:54:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ctV3T97DHjztBGVa5T+lh9QA7Mv+wf84hnNPndqb0Ufpl0nv3YDyh5IK41gDrqMU21L3LCYz/DXXuwyLdhvHAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:36:08.210231Z"},"content_sha256":"ab2d67542d8a3a581f66c828b7c8f74f94c68685a5bdc5ce0aa374f612940a5e","schema_version":"1.0","event_id":"sha256:ab2d67542d8a3a581f66c828b7c8f74f94c68685a5bdc5ce0aa374f612940a5e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2000:XCR7CWPMXDBSUWS64TGSGTO35B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Minimal Models for Non-Free Circle Actions","license":"","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AT","authors_text":"Agusti Roig, Martintxo Saralegi-Aranguren","submitted_at":"2000-04-23T17:27:44Z","abstract_excerpt":"Let $\\Phi \\colon \\sbat \\times M \\to M$ be a smooth action of the unit circle $ \\sbat$ on a manifold $M$. In this work, we compute the minimal model of $M$ in terms of the orbit space $B$ and the fixed point set $F\\subset B$, as a dg-module over the Sullivan's minimal model of $B$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0004141","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":"2026-05-18T03:54:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Utr2rGpokYNyDFzTCtH8TDNJ3OGWBhPCuUG2hRMB2hltqAe1Ut60Ny8dawtcUFzJzfg7fxX5xtJbqpFs7790Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:36:08.210599Z"},"content_sha256":"efb8f2908539ad080c4ab3fd443f59650f84df038f1a408ca40f0246c5e8ecdc","schema_version":"1.0","event_id":"sha256:efb8f2908539ad080c4ab3fd443f59650f84df038f1a408ca40f0246c5e8ecdc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XCR7CWPMXDBSUWS64TGSGTO35B/bundle.json","state_url":"https://pith.science/pith/XCR7CWPMXDBSUWS64TGSGTO35B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XCR7CWPMXDBSUWS64TGSGTO35B/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":"2026-06-23T14:36:08Z","links":{"resolver":"https://pith.science/pith/XCR7CWPMXDBSUWS64TGSGTO35B","bundle":"https://pith.science/pith/XCR7CWPMXDBSUWS64TGSGTO35B/bundle.json","state":"https://pith.science/pith/XCR7CWPMXDBSUWS64TGSGTO35B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XCR7CWPMXDBSUWS64TGSGTO35B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:XCR7CWPMXDBSUWS64TGSGTO35B","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":"d8bfbfa717c55783eac5a78b9ee99921a8f3905e9cb538b8d6c8b9f7be816b2b","cross_cats_sorted":["math.DG"],"license":"","primary_cat":"math.AT","submitted_at":"2000-04-23T17:27:44Z","title_canon_sha256":"3a5a25cd19729643f3e31aa920a313c689af315c707aa80f35beb2556b5bd502"},"schema_version":"1.0","source":{"id":"math/0004141","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0004141","created_at":"2026-05-18T03:54:26Z"},{"alias_kind":"arxiv_version","alias_value":"math/0004141v1","created_at":"2026-05-18T03:54:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0004141","created_at":"2026-05-18T03:54:26Z"},{"alias_kind":"pith_short_12","alias_value":"XCR7CWPMXDBS","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"XCR7CWPMXDBSUWS6","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"XCR7CWPM","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:efb8f2908539ad080c4ab3fd443f59650f84df038f1a408ca40f0246c5e8ecdc","target":"graph","created_at":"2026-05-18T03:54:26Z","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":"Let $\\Phi \\colon \\sbat \\times M \\to M$ be a smooth action of the unit circle $ \\sbat$ on a manifold $M$. In this work, we compute the minimal model of $M$ in terms of the orbit space $B$ and the fixed point set $F\\subset B$, as a dg-module over the Sullivan's minimal model of $B$.","authors_text":"Agusti Roig, Martintxo Saralegi-Aranguren","cross_cats":["math.DG"],"headline":"","license":"","primary_cat":"math.AT","submitted_at":"2000-04-23T17:27:44Z","title":"Minimal Models for Non-Free Circle Actions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0004141","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:ab2d67542d8a3a581f66c828b7c8f74f94c68685a5bdc5ce0aa374f612940a5e","target":"record","created_at":"2026-05-18T03:54:26Z","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":"d8bfbfa717c55783eac5a78b9ee99921a8f3905e9cb538b8d6c8b9f7be816b2b","cross_cats_sorted":["math.DG"],"license":"","primary_cat":"math.AT","submitted_at":"2000-04-23T17:27:44Z","title_canon_sha256":"3a5a25cd19729643f3e31aa920a313c689af315c707aa80f35beb2556b5bd502"},"schema_version":"1.0","source":{"id":"math/0004141","kind":"arxiv","version":1}},"canonical_sha256":"b8a3f159ecb8c32a5a5ee4cd234ddbe86c24dd8afe36ba140982191852a44877","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8a3f159ecb8c32a5a5ee4cd234ddbe86c24dd8afe36ba140982191852a44877","first_computed_at":"2026-05-18T03:54:26.574015Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:26.574015Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GP27vcQqSdMrhztFvvFwRWDlJJEBBU02m0HmMKddqWQaj7fiIAP+BXcsUNLmQEQ2AHn6wet7xYJAwtH+TD2kBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:26.574741Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0004141","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab2d67542d8a3a581f66c828b7c8f74f94c68685a5bdc5ce0aa374f612940a5e","sha256:efb8f2908539ad080c4ab3fd443f59650f84df038f1a408ca40f0246c5e8ecdc"],"state_sha256":"a53e7822ff678b6aa8119f0ddba76432908676142cbde79ec3cb96262c6b81dc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mhSWMq5PuzQ/JztKZqOaaiuHelL2zzorjv30uM/YiXlff3xqAg8TZJ7aRUVlquh+0dv9/MK3XDAZVw1a+V9GDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T14:36:08.212481Z","bundle_sha256":"8bd3057c702d1204cd8074563c8f7cff82535f00f81471ef54b14a619be4a1a5"}}