{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:7CVCSB4JVRXHECNXRXHWPDQUPN","short_pith_number":"pith:7CVCSB4J","canonical_record":{"source":{"id":"2402.06183","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2024-02-09T04:39:10Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"1da981d4d6e301ed2b051c405a4989b5325a0e1bd789c44dccf056d6a39ceeee","abstract_canon_sha256":"30ef10fabbb639ea577275d09b07297e2de7770aee66b3b851961b9ad6c43bef"},"schema_version":"1.0"},"canonical_sha256":"f8aa290789ac6e7209b78dcf678e147b5b62079f1a3f4357ce85281023116b08","source":{"kind":"arxiv","id":"2402.06183","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.06183","created_at":"2026-07-05T08:18:48Z"},{"alias_kind":"arxiv_version","alias_value":"2402.06183v2","created_at":"2026-07-05T08:18:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.06183","created_at":"2026-07-05T08:18:48Z"},{"alias_kind":"pith_short_12","alias_value":"7CVCSB4JVRXH","created_at":"2026-07-05T08:18:48Z"},{"alias_kind":"pith_short_16","alias_value":"7CVCSB4JVRXHECNX","created_at":"2026-07-05T08:18:48Z"},{"alias_kind":"pith_short_8","alias_value":"7CVCSB4J","created_at":"2026-07-05T08:18:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:7CVCSB4JVRXHECNXRXHWPDQUPN","target":"record","payload":{"canonical_record":{"source":{"id":"2402.06183","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2024-02-09T04:39:10Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"1da981d4d6e301ed2b051c405a4989b5325a0e1bd789c44dccf056d6a39ceeee","abstract_canon_sha256":"30ef10fabbb639ea577275d09b07297e2de7770aee66b3b851961b9ad6c43bef"},"schema_version":"1.0"},"canonical_sha256":"f8aa290789ac6e7209b78dcf678e147b5b62079f1a3f4357ce85281023116b08","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:18:48.985220Z","signature_b64":"2uMfeWm9m4piLiqkWI2CzgSDWDmqPAcTaiwiGTTM3Pi6coK2Vbl8YRndyDfdkc8FAI0iQiWfavTChmcEaP8jDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8aa290789ac6e7209b78dcf678e147b5b62079f1a3f4357ce85281023116b08","last_reissued_at":"2026-07-05T08:18:48.984812Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:18:48.984812Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2402.06183","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":"2026-07-05T08:18:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IcVIBPJK8DSc94RdjXpcUnFqZZozlQ1tiClGwopsY0VRBSgHunUWlP2f6e58zRgC14m7VYE8dJaJ73U3orWpBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T16:20:16.421833Z"},"content_sha256":"55ac0393ffa05b0c3e034512b58d334b018f67d21a2913ba5e9bf64fc6bcb234","schema_version":"1.0","event_id":"sha256:55ac0393ffa05b0c3e034512b58d334b018f67d21a2913ba5e9bf64fc6bcb234"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:7CVCSB4JVRXHECNXRXHWPDQUPN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On operadic open-closed maps in characteristic $p$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.SG","authors_text":"Zihong Chen","submitted_at":"2024-02-09T04:39:10Z","abstract_excerpt":"Consider a closed monotone symplectic manifold $(M,\\omega)$. \\cite{Gan2} constructed a cyclic open-closed map, which goes from the cyclic homology of the Fukaya category of $M$ to the $S^1$-equivariant quantum cohomology of $M$. In this paper, we show that with mod $p$ coefficients, Ganatra's cyclic open-closed map is compatible with a certain $\\mathbb{Z}/p$-equivariant open-closed map under the natural $\\mathbb{Z}/p$-Gysin type comparison map for Hochschild homology. Along with the proof, this paper gives a new homotopy theoretic framework for studying open-closed maps in symplectic topology."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.06183","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2402.06183/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":"2026-07-05T08:18:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n+Eu/CK2fqn2+oBU06xb9ew2nu+YEjTsazKwVr68eGocpiHT2cDa1Dp2hwRfU7yru4s+KmCHBOUQmaYZ1EvKCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T16:20:16.422207Z"},"content_sha256":"99b80cb50336e468655bff7329fe9ba16886af90579122b6db328cec614757df","schema_version":"1.0","event_id":"sha256:99b80cb50336e468655bff7329fe9ba16886af90579122b6db328cec614757df"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7CVCSB4JVRXHECNXRXHWPDQUPN/bundle.json","state_url":"https://pith.science/pith/7CVCSB4JVRXHECNXRXHWPDQUPN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7CVCSB4JVRXHECNXRXHWPDQUPN/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":"2026-07-08T16:20:16Z","links":{"resolver":"https://pith.science/pith/7CVCSB4JVRXHECNXRXHWPDQUPN","bundle":"https://pith.science/pith/7CVCSB4JVRXHECNXRXHWPDQUPN/bundle.json","state":"https://pith.science/pith/7CVCSB4JVRXHECNXRXHWPDQUPN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7CVCSB4JVRXHECNXRXHWPDQUPN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:7CVCSB4JVRXHECNXRXHWPDQUPN","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":"30ef10fabbb639ea577275d09b07297e2de7770aee66b3b851961b9ad6c43bef","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2024-02-09T04:39:10Z","title_canon_sha256":"1da981d4d6e301ed2b051c405a4989b5325a0e1bd789c44dccf056d6a39ceeee"},"schema_version":"1.0","source":{"id":"2402.06183","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.06183","created_at":"2026-07-05T08:18:48Z"},{"alias_kind":"arxiv_version","alias_value":"2402.06183v2","created_at":"2026-07-05T08:18:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.06183","created_at":"2026-07-05T08:18:48Z"},{"alias_kind":"pith_short_12","alias_value":"7CVCSB4JVRXH","created_at":"2026-07-05T08:18:48Z"},{"alias_kind":"pith_short_16","alias_value":"7CVCSB4JVRXHECNX","created_at":"2026-07-05T08:18:48Z"},{"alias_kind":"pith_short_8","alias_value":"7CVCSB4J","created_at":"2026-07-05T08:18:48Z"}],"graph_snapshots":[{"event_id":"sha256:99b80cb50336e468655bff7329fe9ba16886af90579122b6db328cec614757df","target":"graph","created_at":"2026-07-05T08:18:48Z","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/2402.06183/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Consider a closed monotone symplectic manifold $(M,\\omega)$. \\cite{Gan2} constructed a cyclic open-closed map, which goes from the cyclic homology of the Fukaya category of $M$ to the $S^1$-equivariant quantum cohomology of $M$. In this paper, we show that with mod $p$ coefficients, Ganatra's cyclic open-closed map is compatible with a certain $\\mathbb{Z}/p$-equivariant open-closed map under the natural $\\mathbb{Z}/p$-Gysin type comparison map for Hochschild homology. Along with the proof, this paper gives a new homotopy theoretic framework for studying open-closed maps in symplectic topology.","authors_text":"Zihong Chen","cross_cats":["math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2024-02-09T04:39:10Z","title":"On operadic open-closed maps in characteristic $p$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.06183","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":"sha256:55ac0393ffa05b0c3e034512b58d334b018f67d21a2913ba5e9bf64fc6bcb234","target":"record","created_at":"2026-07-05T08:18:48Z","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":"30ef10fabbb639ea577275d09b07297e2de7770aee66b3b851961b9ad6c43bef","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2024-02-09T04:39:10Z","title_canon_sha256":"1da981d4d6e301ed2b051c405a4989b5325a0e1bd789c44dccf056d6a39ceeee"},"schema_version":"1.0","source":{"id":"2402.06183","kind":"arxiv","version":2}},"canonical_sha256":"f8aa290789ac6e7209b78dcf678e147b5b62079f1a3f4357ce85281023116b08","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8aa290789ac6e7209b78dcf678e147b5b62079f1a3f4357ce85281023116b08","first_computed_at":"2026-07-05T08:18:48.984812Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:18:48.984812Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2uMfeWm9m4piLiqkWI2CzgSDWDmqPAcTaiwiGTTM3Pi6coK2Vbl8YRndyDfdkc8FAI0iQiWfavTChmcEaP8jDA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:18:48.985220Z","signed_message":"canonical_sha256_bytes"},"source_id":"2402.06183","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:55ac0393ffa05b0c3e034512b58d334b018f67d21a2913ba5e9bf64fc6bcb234","sha256:99b80cb50336e468655bff7329fe9ba16886af90579122b6db328cec614757df"],"state_sha256":"4c6432f0a69e23a65b5426caf1fbf1cbcd14e9593666f1d94296eb8d1bf2021f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NtGpvU9jBIVeF6nKVWumtuRPo+TCQCb1tPiSKWwZ984P2d5adCZsE9bMuYgIi93nhHkveblMd2ceLFI73e+EBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-08T16:20:16.424299Z","bundle_sha256":"e571369703d68195179780e85fac08c7763e174681fab4449b1bfb2236377056"}}