{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:IVGFM33V6BT76T5K2IOKT2RLOE","short_pith_number":"pith:IVGFM33V","canonical_record":{"source":{"id":"2209.08599","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SG","submitted_at":"2022-09-18T16:30:15Z","cross_cats_sorted":["math.AT","math.DS","math.GT"],"title_canon_sha256":"6e382142256997c9aa180679bbfc727aa99b819257bb2f89bb48264b64663743","abstract_canon_sha256":"68f3129cf6c3d988076f6a3c90352c61c1e59921f3aeb51bce973cd41a681400"},"schema_version":"1.0"},"canonical_sha256":"454c566f75f067ff4faad21ca9ea2b71327f4d75ec0c03c2e9d0d39b3b79fe93","source":{"kind":"arxiv","id":"2209.08599","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.08599","created_at":"2026-07-05T04:58:43Z"},{"alias_kind":"arxiv_version","alias_value":"2209.08599v1","created_at":"2026-07-05T04:58:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.08599","created_at":"2026-07-05T04:58:43Z"},{"alias_kind":"pith_short_12","alias_value":"IVGFM33V6BT7","created_at":"2026-07-05T04:58:43Z"},{"alias_kind":"pith_short_16","alias_value":"IVGFM33V6BT76T5K","created_at":"2026-07-05T04:58:43Z"},{"alias_kind":"pith_short_8","alias_value":"IVGFM33V","created_at":"2026-07-05T04:58:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:IVGFM33V6BT76T5K2IOKT2RLOE","target":"record","payload":{"canonical_record":{"source":{"id":"2209.08599","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SG","submitted_at":"2022-09-18T16:30:15Z","cross_cats_sorted":["math.AT","math.DS","math.GT"],"title_canon_sha256":"6e382142256997c9aa180679bbfc727aa99b819257bb2f89bb48264b64663743","abstract_canon_sha256":"68f3129cf6c3d988076f6a3c90352c61c1e59921f3aeb51bce973cd41a681400"},"schema_version":"1.0"},"canonical_sha256":"454c566f75f067ff4faad21ca9ea2b71327f4d75ec0c03c2e9d0d39b3b79fe93","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:58:43.451633Z","signature_b64":"f9kv/EReRNQX84J5jcIjvTfcd+j/0uHrT+zRupI2Uk0AEZ+WxzqRMJGt+QEM4dxtsnHiKjXjZjRNp9EVusN+Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"454c566f75f067ff4faad21ca9ea2b71327f4d75ec0c03c2e9d0d39b3b79fe93","last_reissued_at":"2026-07-05T04:58:43.451151Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:58:43.451151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2209.08599","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":"2026-07-05T04:58:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"McOZ2FtIy/1sMkbDVGl8UyXkZErerCnwpXLZT9gPCi5BqfqZT/yT6WuN0W34eZ3X61T6sdiFNAs47e/QHPiGCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T09:59:38.504866Z"},"content_sha256":"a16af6c7d75ef640de5daa606f9077f085d3b8c9226329762c2a81ab831538bd","schema_version":"1.0","event_id":"sha256:a16af6c7d75ef640de5daa606f9077f085d3b8c9226329762c2a81ab831538bd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:IVGFM33V6BT76T5K2IOKT2RLOE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Arnold conjecture over integers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AT","math.DS","math.GT"],"primary_cat":"math.SG","authors_text":"Guangbo Xu, Shaoyun Bai","submitted_at":"2022-09-18T16:30:15Z","abstract_excerpt":"For any closed symplectic manifold, we show that the number of 1-periodic orbits of a nondegenerate Hamiltonian thereon is bounded from below by a version of total Betti number over Z of the ambient space taking account of the total Betti number over Q and torsions of all characteristic. The proof is based on constructing a Hamiltonian Floer theory over the Novikov ring with integer coefficients, which generalizes our earlier work for constructing integer-valued Gromov-Witten type invariants. In the course of the construction, we build a Hamiltonian Floer flow category with compatible smooth g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.08599","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2209.08599/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":"2026-07-05T04:58:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5idknMzuPY9oU/TKtkoiHzDjgQzmD2UlDFzeBWmET7xzrNK0bA4y/TIpTuWayoHRLKeGqBgG/3lT86fOlFBaCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T09:59:38.505458Z"},"content_sha256":"64db227dc91d64474c1d144e21962e85bf65e46ac5942fe7f7ac52ff90c9a3d6","schema_version":"1.0","event_id":"sha256:64db227dc91d64474c1d144e21962e85bf65e46ac5942fe7f7ac52ff90c9a3d6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IVGFM33V6BT76T5K2IOKT2RLOE/bundle.json","state_url":"https://pith.science/pith/IVGFM33V6BT76T5K2IOKT2RLOE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IVGFM33V6BT76T5K2IOKT2RLOE/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":"2026-08-04T09:59:38Z","links":{"resolver":"https://pith.science/pith/IVGFM33V6BT76T5K2IOKT2RLOE","bundle":"https://pith.science/pith/IVGFM33V6BT76T5K2IOKT2RLOE/bundle.json","state":"https://pith.science/pith/IVGFM33V6BT76T5K2IOKT2RLOE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IVGFM33V6BT76T5K2IOKT2RLOE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:IVGFM33V6BT76T5K2IOKT2RLOE","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":"68f3129cf6c3d988076f6a3c90352c61c1e59921f3aeb51bce973cd41a681400","cross_cats_sorted":["math.AT","math.DS","math.GT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SG","submitted_at":"2022-09-18T16:30:15Z","title_canon_sha256":"6e382142256997c9aa180679bbfc727aa99b819257bb2f89bb48264b64663743"},"schema_version":"1.0","source":{"id":"2209.08599","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.08599","created_at":"2026-07-05T04:58:43Z"},{"alias_kind":"arxiv_version","alias_value":"2209.08599v1","created_at":"2026-07-05T04:58:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.08599","created_at":"2026-07-05T04:58:43Z"},{"alias_kind":"pith_short_12","alias_value":"IVGFM33V6BT7","created_at":"2026-07-05T04:58:43Z"},{"alias_kind":"pith_short_16","alias_value":"IVGFM33V6BT76T5K","created_at":"2026-07-05T04:58:43Z"},{"alias_kind":"pith_short_8","alias_value":"IVGFM33V","created_at":"2026-07-05T04:58:43Z"}],"graph_snapshots":[{"event_id":"sha256:64db227dc91d64474c1d144e21962e85bf65e46ac5942fe7f7ac52ff90c9a3d6","target":"graph","created_at":"2026-07-05T04:58:43Z","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/2209.08599/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For any closed symplectic manifold, we show that the number of 1-periodic orbits of a nondegenerate Hamiltonian thereon is bounded from below by a version of total Betti number over Z of the ambient space taking account of the total Betti number over Q and torsions of all characteristic. The proof is based on constructing a Hamiltonian Floer theory over the Novikov ring with integer coefficients, which generalizes our earlier work for constructing integer-valued Gromov-Witten type invariants. In the course of the construction, we build a Hamiltonian Floer flow category with compatible smooth g","authors_text":"Guangbo Xu, Shaoyun Bai","cross_cats":["math.AT","math.DS","math.GT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SG","submitted_at":"2022-09-18T16:30:15Z","title":"Arnold conjecture over integers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.08599","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:a16af6c7d75ef640de5daa606f9077f085d3b8c9226329762c2a81ab831538bd","target":"record","created_at":"2026-07-05T04:58:43Z","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":"68f3129cf6c3d988076f6a3c90352c61c1e59921f3aeb51bce973cd41a681400","cross_cats_sorted":["math.AT","math.DS","math.GT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SG","submitted_at":"2022-09-18T16:30:15Z","title_canon_sha256":"6e382142256997c9aa180679bbfc727aa99b819257bb2f89bb48264b64663743"},"schema_version":"1.0","source":{"id":"2209.08599","kind":"arxiv","version":1}},"canonical_sha256":"454c566f75f067ff4faad21ca9ea2b71327f4d75ec0c03c2e9d0d39b3b79fe93","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"454c566f75f067ff4faad21ca9ea2b71327f4d75ec0c03c2e9d0d39b3b79fe93","first_computed_at":"2026-07-05T04:58:43.451151Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:58:43.451151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f9kv/EReRNQX84J5jcIjvTfcd+j/0uHrT+zRupI2Uk0AEZ+WxzqRMJGt+QEM4dxtsnHiKjXjZjRNp9EVusN+Bw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:58:43.451633Z","signed_message":"canonical_sha256_bytes"},"source_id":"2209.08599","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a16af6c7d75ef640de5daa606f9077f085d3b8c9226329762c2a81ab831538bd","sha256:64db227dc91d64474c1d144e21962e85bf65e46ac5942fe7f7ac52ff90c9a3d6"],"state_sha256":"75fd9d977f25f036ea82ee4281ca34aa4df21fcef0b4b330067c52d70cf633d9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cP7cTGvPvjJ2Nywd+Uk11vj3HPfAXaR67C3Iqv66chjzAVfcfr51H0avh656bebAjs7/F7zt09xvEHojJ4EaCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T09:59:38.510278Z","bundle_sha256":"e56d110debb03ff0362ca4b33c5c81feedc4f99d638849a25d4073024d931a4f"}}