{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:AGGG36H6DCXIOBBXFXVSDQZTPP","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":"c4550aeae42392edaa47cab840888e99cb69fb11cff982a5586c918ad1457786","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-08-15T17:02:01Z","title_canon_sha256":"a58483148ab9f130fd43b398c609fa3667013820592048192adcef66b50715be"},"schema_version":"1.0","source":{"id":"1308.3456","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.3456","created_at":"2026-05-18T02:53:53Z"},{"alias_kind":"arxiv_version","alias_value":"1308.3456v3","created_at":"2026-05-18T02:53:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.3456","created_at":"2026-05-18T02:53:53Z"},{"alias_kind":"pith_short_12","alias_value":"AGGG36H6DCXI","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"AGGG36H6DCXIOBBX","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"AGGG36H6","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:c18372faf6df1a611bd5efd8b40abfdb421c7578bc2aba2d005664d614bd0f37","target":"graph","created_at":"2026-05-18T02:53:53Z","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":"Following \\cite{citeSavelyevVirtualMorsetheoryon$Omega$Ham$(Momega)$.}, we develop here a connection between Morse theory for the (positive) Hofer length functional $L: \\Omega \\text {Ham}(M, \\omega) \\to \\mathbb{R}$, with Gromov-Witten/Floer theory, for monotone symplectic manifolds $ (M, \\omega) $. This gives some immediate restrictions on the topology of the group of Hamiltonian symplectomorphisms (possibly relative to the Hofer length functional), and a criterion for non-existence of certain higher index geodesics for the Hofer length functional. The argument is based on a certain automatic ","authors_text":"Yasha Savelyev","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-08-15T17:02:01Z","title":"Morse theory for the Hofer length functional"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3456","kind":"arxiv","version":3},"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":"sha256:165bd7901982754cad5bf1a90084983b703bf16780c83b2a1d064778868fca10","target":"record","created_at":"2026-05-18T02:53:53Z","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":"c4550aeae42392edaa47cab840888e99cb69fb11cff982a5586c918ad1457786","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-08-15T17:02:01Z","title_canon_sha256":"a58483148ab9f130fd43b398c609fa3667013820592048192adcef66b50715be"},"schema_version":"1.0","source":{"id":"1308.3456","kind":"arxiv","version":3}},"canonical_sha256":"018c6df8fe18ae8704372deb21c3337bf32c323307b210f6eb92e7cfac6081de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"018c6df8fe18ae8704372deb21c3337bf32c323307b210f6eb92e7cfac6081de","first_computed_at":"2026-05-18T02:53:53.668784Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:53:53.668784Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RYaQZH+Q67twgmxg3DbVczjPdr122IbWJKC63KsxtOOj4TYnktxQNQiPg0Zo4loKO3PNc2+eqaziEoMYROQbCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:53:53.669601Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.3456","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:165bd7901982754cad5bf1a90084983b703bf16780c83b2a1d064778868fca10","sha256:c18372faf6df1a611bd5efd8b40abfdb421c7578bc2aba2d005664d614bd0f37"],"state_sha256":"5e838fdd6271888abe6067ee45f82bfc34118155902295b9d410f80c22f511b2"}