{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:V66HNW25AN2IW65BVD6TMC36KJ","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":"cea90ace377ae8cb966401fba9bf6a6643f0545db7cf5bf54c91e85698b899fe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-10-23T19:18:02Z","title_canon_sha256":"481362ea37bdb9b2f7a076a3949b92e068fb9a1420582ec262626bdd7fe3a88f"},"schema_version":"1.0","source":{"id":"1410.6458","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.6458","created_at":"2026-05-18T01:18:25Z"},{"alias_kind":"arxiv_version","alias_value":"1410.6458v2","created_at":"2026-05-18T01:18:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.6458","created_at":"2026-05-18T01:18:25Z"},{"alias_kind":"pith_short_12","alias_value":"V66HNW25AN2I","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"V66HNW25AN2IW65B","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"V66HNW25","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:4b637e658e8688e03b08d8f4284749c2f1956fbe2d1260fb24eb65bc7e2b7a89","target":"graph","created_at":"2026-05-18T01:18:25Z","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":"Growth of the Hilbert-Poincar\\\"e series for the rational homology of the free loop space of a toric space is addressed. In case the toric space is a manifold, the structure of the fan dictates whether the Hilbert-Poincar\\\"e series has exponential growth. Applications are made to the existence of infinitely many geometrically distinct periodic geodesics.","authors_text":"A. Bahri, F. R. Cohen, M. Bendersky, S. Gitler","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-10-23T19:18:02Z","title":"On free loop spaces of toric spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6458","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:a3eab5ad2a3ab11fae1c046e653bbf78d61c448b79f5cddd7a04da1851ec0711","target":"record","created_at":"2026-05-18T01:18:25Z","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":"cea90ace377ae8cb966401fba9bf6a6643f0545db7cf5bf54c91e85698b899fe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-10-23T19:18:02Z","title_canon_sha256":"481362ea37bdb9b2f7a076a3949b92e068fb9a1420582ec262626bdd7fe3a88f"},"schema_version":"1.0","source":{"id":"1410.6458","kind":"arxiv","version":2}},"canonical_sha256":"afbc76db5d03748b7ba1a8fd360b7e527397243fe52770801416be53394613d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"afbc76db5d03748b7ba1a8fd360b7e527397243fe52770801416be53394613d2","first_computed_at":"2026-05-18T01:18:25.698274Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:25.698274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SFp2UMU0DnjluF5tAd+JeDQhJ2Guo1foxzsyT5CIxSfbwxaZoZIAqzEjIfiLvufnnLsI4I/nWHCYXZFFF/N8CA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:25.698860Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.6458","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a3eab5ad2a3ab11fae1c046e653bbf78d61c448b79f5cddd7a04da1851ec0711","sha256:4b637e658e8688e03b08d8f4284749c2f1956fbe2d1260fb24eb65bc7e2b7a89"],"state_sha256":"ae2ecdcf8bf62f19f6da359e0c77885c74f602ff3b39b37b1f399a49a7485ef0"}