{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:M5EQFLE3VLWO7XISWKOPVHAJLX","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":"fd81bdb8d59fe9843695834e92f168cc4f75f965af3b77056fafa6d1c4ea98ad","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-07-19T17:16:24Z","title_canon_sha256":"a6e11448c456da63137275fa4093bde98cacbc51965b9b922370db94b2f6b910"},"schema_version":"1.0","source":{"id":"1007.3213","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.3213","created_at":"2026-05-18T04:20:13Z"},{"alias_kind":"arxiv_version","alias_value":"1007.3213v6","created_at":"2026-05-18T04:20:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.3213","created_at":"2026-05-18T04:20:13Z"},{"alias_kind":"pith_short_12","alias_value":"M5EQFLE3VLWO","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"M5EQFLE3VLWO7XIS","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"M5EQFLE3","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:90bb6f3bb3c0f7752e0e2224412c966158dfb84f00436f088c2dfc33f7778003","target":"graph","created_at":"2026-05-18T04:20:13Z","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":"We introduce here a natural functional associated to any $b \\in QH_* (M, \\omega)$: \\emph{spectral length functional}, on the space of \"generalized paths\" in $ \\text {Ham}(M, \\omega)$, closely related to both the Hofer length functional and spectral invariants and establish some of its properties. This functional is smooth on its domain of definition, and moreover the nature of extremals of this functional suggests that it may be variationally complete, in the sense that any suitably generic element of $ \\widetilde{\\text {Ham}}(M, \\omega)$ is connected to $id$ by a generalized path minimizing s","authors_text":"Yasha Savelyev","cross_cats":["math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-07-19T17:16:24Z","title":"Spectral geometry of the group of Hamiltonian symplectomorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.3213","kind":"arxiv","version":6},"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":"sha256:0b27a97dd1a036b9fe6e0e3ab401daa672c06310bb9864a3714f22d386edb4f2","target":"record","created_at":"2026-05-18T04:20:13Z","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":"fd81bdb8d59fe9843695834e92f168cc4f75f965af3b77056fafa6d1c4ea98ad","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-07-19T17:16:24Z","title_canon_sha256":"a6e11448c456da63137275fa4093bde98cacbc51965b9b922370db94b2f6b910"},"schema_version":"1.0","source":{"id":"1007.3213","kind":"arxiv","version":6}},"canonical_sha256":"674902ac9baaecefdd12b29cfa9c095dc4c3170e4a7f6b8b9a6859c5f6445124","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"674902ac9baaecefdd12b29cfa9c095dc4c3170e4a7f6b8b9a6859c5f6445124","first_computed_at":"2026-05-18T04:20:13.151276Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:13.151276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2Xc2ypiQyEG1UPI3Tg90MEtlEJFfy+IGAck5GZijmEa/HUIYUhazIOQoPbMParsf6IHJ3iqbupsIkyL3OoUeAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:13.151910Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.3213","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b27a97dd1a036b9fe6e0e3ab401daa672c06310bb9864a3714f22d386edb4f2","sha256:90bb6f3bb3c0f7752e0e2224412c966158dfb84f00436f088c2dfc33f7778003"],"state_sha256":"b1511b103193d59e4002b3b38b474bb9f5a3a49123969325c7af382d83d1992c"}