{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4HVCHDKYHURHRAPVA3DYFKX565","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":"fc1cbbe62abee421ab2f76528bb7ba6e81c9877d07d31bc8b1eb3d03b06e5459","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2016-02-18T15:38:08Z","title_canon_sha256":"d201bbcafcf06299a41fd4540ead4559c0b61ba8ea40d0da2bad1150aec35be4"},"schema_version":"1.0","source":{"id":"1602.05842","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.05842","created_at":"2026-05-18T00:28:19Z"},{"alias_kind":"arxiv_version","alias_value":"1602.05842v2","created_at":"2026-05-18T00:28:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.05842","created_at":"2026-05-18T00:28:19Z"},{"alias_kind":"pith_short_12","alias_value":"4HVCHDKYHURH","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4HVCHDKYHURHRAPV","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4HVCHDKY","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:b58c87b20c933cc9bd95432b00868facf7f20a2c4eb500d46ff3907d205f892d","target":"graph","created_at":"2026-05-18T00:28:19Z","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":"Given a symplectic surface $(\\Sigma, \\omega)$ of genus $g \\ge 4$, we show that the free group with two generators embeds into every asymptotic cone of $(\\mathrm{Ham}(\\Sigma, \\omega), d_\\mathrm{H})$, where $d_\\mathrm{H}$ is the Hofer metric. The result stabilizes to products with symplectically aspherical manifolds.","authors_text":"Andrei Pavlichenko, Asaf Kislev, Bret Stevenson, Daniel Alvarez-Gavela, Daniel Rosen, Jun Zhang, Konstantin Kliakhandler, Lorenzo Rigolli, Ood Shabtai, Victoria Kaminker","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2016-02-18T15:38:08Z","title":"Embeddings of free groups into asymptotic cones of Hamiltonian diffeomorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05842","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":"sha256:1aefd5dbee8d8dd3bbfbeed32ab96b73024562f2cc79e6f6bee0c0555840429a","target":"record","created_at":"2026-05-18T00:28:19Z","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":"fc1cbbe62abee421ab2f76528bb7ba6e81c9877d07d31bc8b1eb3d03b06e5459","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2016-02-18T15:38:08Z","title_canon_sha256":"d201bbcafcf06299a41fd4540ead4559c0b61ba8ea40d0da2bad1150aec35be4"},"schema_version":"1.0","source":{"id":"1602.05842","kind":"arxiv","version":2}},"canonical_sha256":"e1ea238d583d227881f506c782aafdf76b91cb63ecd23c6cf54256864abb3490","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e1ea238d583d227881f506c782aafdf76b91cb63ecd23c6cf54256864abb3490","first_computed_at":"2026-05-18T00:28:19.037204Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:19.037204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e24p4keYaF9i8nCuGUtGTqtqmGITfOffDkQTqvri2EjSaRZjW5k3dYFVhdbE4oQUp8En8LNts+iF8Q/W/uh+Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:19.038015Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.05842","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1aefd5dbee8d8dd3bbfbeed32ab96b73024562f2cc79e6f6bee0c0555840429a","sha256:b58c87b20c933cc9bd95432b00868facf7f20a2c4eb500d46ff3907d205f892d"],"state_sha256":"4653a0b3118330c14ed0000dc18111e0034f030226a030430b881a7aaebc1fac"}