{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:CP7TEYZHXMAXTWH35JHNXXJZXB","short_pith_number":"pith:CP7TEYZH","schema_version":"1.0","canonical_sha256":"13ff326327bb0179d8fbea4edbdd39b878bc516355324396d34ff8fbbb5be4b6","source":{"kind":"arxiv","id":"1501.02740","version":3},"attestation_state":"computed","paper":{"title":"On the Hofer geometry injectivity radius conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SG","authors_text":"Yasha Savelyev","submitted_at":"2015-01-12T18:03:36Z","abstract_excerpt":"We verify here some variants of topological and dynamical flavor of the injectivity radius conjecture in Hofer geometry, Lalonde-Savelyev \\cite{citeLalondeSavelyevOntheinjectivityradiusinHofergeometry} in the case of $Ham (S^2)$ and $Ham(\\Sigma, \\omega)$, for $\\Sigma$ a closed positive genus surface. In particular we show that any loop in $Ham (S^2)$, respectively $Ham(\\Sigma, \\omega)$ with $L ^{+}$ Hofer length less than $area(S ^{2} )/2$, respectively any $L ^{+} $ length is contractible through ($L ^{+} $) Hofer shorter loops, in the $C ^{\\infty} $ topology. We also prove some stronger vari"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1501.02740","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-01-12T18:03:36Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"ac6286ce5a2e7cb57d135208c9c90d61ebdb288ccb11e57803a67071c6dc37a4","abstract_canon_sha256":"aee4fb5c149ebcf0f4e3e7ed2a7ddadfa515153befabe0d83ffe37b4c89351f9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:13.590608Z","signature_b64":"T64JygJsJYkEjFiEhegt0ZkDEZ4YA3vz+Fh7IMFabkMGLQptVSWdmz3gQy1+GNAR0A0F+nxHIECxHwW6mc4bBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13ff326327bb0179d8fbea4edbdd39b878bc516355324396d34ff8fbbb5be4b6","last_reissued_at":"2026-05-18T01:21:13.589946Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:13.589946Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Hofer geometry injectivity radius conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SG","authors_text":"Yasha Savelyev","submitted_at":"2015-01-12T18:03:36Z","abstract_excerpt":"We verify here some variants of topological and dynamical flavor of the injectivity radius conjecture in Hofer geometry, Lalonde-Savelyev \\cite{citeLalondeSavelyevOntheinjectivityradiusinHofergeometry} in the case of $Ham (S^2)$ and $Ham(\\Sigma, \\omega)$, for $\\Sigma$ a closed positive genus surface. In particular we show that any loop in $Ham (S^2)$, respectively $Ham(\\Sigma, \\omega)$ with $L ^{+}$ Hofer length less than $area(S ^{2} )/2$, respectively any $L ^{+} $ length is contractible through ($L ^{+} $) Hofer shorter loops, in the $C ^{\\infty} $ topology. We also prove some stronger vari"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02740","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1501.02740","created_at":"2026-05-18T01:21:13.590046+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.02740v3","created_at":"2026-05-18T01:21:13.590046+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.02740","created_at":"2026-05-18T01:21:13.590046+00:00"},{"alias_kind":"pith_short_12","alias_value":"CP7TEYZHXMAX","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_16","alias_value":"CP7TEYZHXMAXTWH3","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_8","alias_value":"CP7TEYZH","created_at":"2026-05-18T12:29:17.054201+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CP7TEYZHXMAXTWH35JHNXXJZXB","json":"https://pith.science/pith/CP7TEYZHXMAXTWH35JHNXXJZXB.json","graph_json":"https://pith.science/api/pith-number/CP7TEYZHXMAXTWH35JHNXXJZXB/graph.json","events_json":"https://pith.science/api/pith-number/CP7TEYZHXMAXTWH35JHNXXJZXB/events.json","paper":"https://pith.science/paper/CP7TEYZH"},"agent_actions":{"view_html":"https://pith.science/pith/CP7TEYZHXMAXTWH35JHNXXJZXB","download_json":"https://pith.science/pith/CP7TEYZHXMAXTWH35JHNXXJZXB.json","view_paper":"https://pith.science/paper/CP7TEYZH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.02740&json=true","fetch_graph":"https://pith.science/api/pith-number/CP7TEYZHXMAXTWH35JHNXXJZXB/graph.json","fetch_events":"https://pith.science/api/pith-number/CP7TEYZHXMAXTWH35JHNXXJZXB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CP7TEYZHXMAXTWH35JHNXXJZXB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CP7TEYZHXMAXTWH35JHNXXJZXB/action/storage_attestation","attest_author":"https://pith.science/pith/CP7TEYZHXMAXTWH35JHNXXJZXB/action/author_attestation","sign_citation":"https://pith.science/pith/CP7TEYZHXMAXTWH35JHNXXJZXB/action/citation_signature","submit_replication":"https://pith.science/pith/CP7TEYZHXMAXTWH35JHNXXJZXB/action/replication_record"}},"created_at":"2026-05-18T01:21:13.590046+00:00","updated_at":"2026-05-18T01:21:13.590046+00:00"}