{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:UNXIQSW766ZTLRDSCH7VELCAB5","short_pith_number":"pith:UNXIQSW7","canonical_record":{"source":{"id":"1604.06953","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-04-23T21:00:13Z","cross_cats_sorted":["math-ph","math.DG","math.DS","math.MP","math.SG"],"title_canon_sha256":"daf429638a5ee96ea736296168b90e2e1b3cde1a9c3ff04d45af3e7f688000f1","abstract_canon_sha256":"bf388d86f70308ae5459cb2bd2da45701ec3c1e88a08f8a7d3576b47be4d2cb6"},"schema_version":"1.0"},"canonical_sha256":"a36e884adff7b335c47211ff522c400f77131c6aa80210452a026e806aa61abb","source":{"kind":"arxiv","id":"1604.06953","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.06953","created_at":"2026-05-18T00:20:59Z"},{"alias_kind":"arxiv_version","alias_value":"1604.06953v2","created_at":"2026-05-18T00:20:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06953","created_at":"2026-05-18T00:20:59Z"},{"alias_kind":"pith_short_12","alias_value":"UNXIQSW766ZT","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UNXIQSW766ZTLRDS","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UNXIQSW7","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:UNXIQSW766ZTLRDSCH7VELCAB5","target":"record","payload":{"canonical_record":{"source":{"id":"1604.06953","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-04-23T21:00:13Z","cross_cats_sorted":["math-ph","math.DG","math.DS","math.MP","math.SG"],"title_canon_sha256":"daf429638a5ee96ea736296168b90e2e1b3cde1a9c3ff04d45af3e7f688000f1","abstract_canon_sha256":"bf388d86f70308ae5459cb2bd2da45701ec3c1e88a08f8a7d3576b47be4d2cb6"},"schema_version":"1.0"},"canonical_sha256":"a36e884adff7b335c47211ff522c400f77131c6aa80210452a026e806aa61abb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:59.576739Z","signature_b64":"oJ5e+hCdH34lsjzAxeXO9MxOkn88HQyG4OXZ5bnlFsWLjyYrgrY6G/T4IlavWOzPOag+hDcLhXLO0oN0eCA6Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a36e884adff7b335c47211ff522c400f77131c6aa80210452a026e806aa61abb","last_reissued_at":"2026-05-18T00:20:59.576149Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:59.576149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.06953","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:20:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C/Jgv7ot/QPTxPfmKE+pk/fHegWE68Wx/9sTyU9+HEoqdr8cFCaphZuwKK96Aixu8zZntyIBX+S4Kge8G67mCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:01:31.490041Z"},"content_sha256":"082452082e76a9d239a7d9ae03023ffc79b8e5bc804692c7bb95f78b9b4a81b3","schema_version":"1.0","event_id":"sha256:082452082e76a9d239a7d9ae03023ffc79b8e5bc804692c7bb95f78b9b4a81b3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:UNXIQSW766ZTLRDSCH7VELCAB5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The $L^p$-diameter of the group of area-preserving diffeomorphisms of $S^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DG","math.DS","math.MP","math.SG"],"primary_cat":"math.GT","authors_text":"Egor Shelukhin, Michael Brandenbursky","submitted_at":"2016-04-23T21:00:13Z","abstract_excerpt":"We show that for each $p \\geq 1,$ the $L^p$-metric on the group of area-preserving diffeomorphisms of the two-sphere has infinite diameter. This solves the last open case of a conjecture of Shnirelman from 1985. Our methods extend to yield stronger results on the large-scale geometry of the corresponding metric space, completing an answer to a question of Kapovich from 2012. Our proof uses configuration spaces of points on the two-sphere, quasi-morphisms, optimally chosen braid diagrams, and, as a key element, the cross-ratio map $X_4(\\mathbb{C} P^1) \\to \\mathcal{M}_{0,4} \\cong \\mathbb{C} P^1 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06953","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:20:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1F+725OKgY8TvvUO76zGdolbRKHUzdEqAGtrTjUEb4PbvJ8XYDONQpXF5uzLRoU+xrOHE5CNaF7UOrT/ku1MBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:01:31.490405Z"},"content_sha256":"9bfec83816d3b4d9154834ef78efab1457340d630b18f510f03bc5734afbbc4e","schema_version":"1.0","event_id":"sha256:9bfec83816d3b4d9154834ef78efab1457340d630b18f510f03bc5734afbbc4e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UNXIQSW766ZTLRDSCH7VELCAB5/bundle.json","state_url":"https://pith.science/pith/UNXIQSW766ZTLRDSCH7VELCAB5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UNXIQSW766ZTLRDSCH7VELCAB5/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-20T06:01:31Z","links":{"resolver":"https://pith.science/pith/UNXIQSW766ZTLRDSCH7VELCAB5","bundle":"https://pith.science/pith/UNXIQSW766ZTLRDSCH7VELCAB5/bundle.json","state":"https://pith.science/pith/UNXIQSW766ZTLRDSCH7VELCAB5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UNXIQSW766ZTLRDSCH7VELCAB5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:UNXIQSW766ZTLRDSCH7VELCAB5","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":"bf388d86f70308ae5459cb2bd2da45701ec3c1e88a08f8a7d3576b47be4d2cb6","cross_cats_sorted":["math-ph","math.DG","math.DS","math.MP","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-04-23T21:00:13Z","title_canon_sha256":"daf429638a5ee96ea736296168b90e2e1b3cde1a9c3ff04d45af3e7f688000f1"},"schema_version":"1.0","source":{"id":"1604.06953","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.06953","created_at":"2026-05-18T00:20:59Z"},{"alias_kind":"arxiv_version","alias_value":"1604.06953v2","created_at":"2026-05-18T00:20:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06953","created_at":"2026-05-18T00:20:59Z"},{"alias_kind":"pith_short_12","alias_value":"UNXIQSW766ZT","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UNXIQSW766ZTLRDS","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UNXIQSW7","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:9bfec83816d3b4d9154834ef78efab1457340d630b18f510f03bc5734afbbc4e","target":"graph","created_at":"2026-05-18T00:20:59Z","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 show that for each $p \\geq 1,$ the $L^p$-metric on the group of area-preserving diffeomorphisms of the two-sphere has infinite diameter. This solves the last open case of a conjecture of Shnirelman from 1985. Our methods extend to yield stronger results on the large-scale geometry of the corresponding metric space, completing an answer to a question of Kapovich from 2012. Our proof uses configuration spaces of points on the two-sphere, quasi-morphisms, optimally chosen braid diagrams, and, as a key element, the cross-ratio map $X_4(\\mathbb{C} P^1) \\to \\mathcal{M}_{0,4} \\cong \\mathbb{C} P^1 ","authors_text":"Egor Shelukhin, Michael Brandenbursky","cross_cats":["math-ph","math.DG","math.DS","math.MP","math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-04-23T21:00:13Z","title":"The $L^p$-diameter of the group of area-preserving diffeomorphisms of $S^2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06953","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":"sha256:082452082e76a9d239a7d9ae03023ffc79b8e5bc804692c7bb95f78b9b4a81b3","target":"record","created_at":"2026-05-18T00:20:59Z","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":"bf388d86f70308ae5459cb2bd2da45701ec3c1e88a08f8a7d3576b47be4d2cb6","cross_cats_sorted":["math-ph","math.DG","math.DS","math.MP","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-04-23T21:00:13Z","title_canon_sha256":"daf429638a5ee96ea736296168b90e2e1b3cde1a9c3ff04d45af3e7f688000f1"},"schema_version":"1.0","source":{"id":"1604.06953","kind":"arxiv","version":2}},"canonical_sha256":"a36e884adff7b335c47211ff522c400f77131c6aa80210452a026e806aa61abb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a36e884adff7b335c47211ff522c400f77131c6aa80210452a026e806aa61abb","first_computed_at":"2026-05-18T00:20:59.576149Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:59.576149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oJ5e+hCdH34lsjzAxeXO9MxOkn88HQyG4OXZ5bnlFsWLjyYrgrY6G/T4IlavWOzPOag+hDcLhXLO0oN0eCA6Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:59.576739Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.06953","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:082452082e76a9d239a7d9ae03023ffc79b8e5bc804692c7bb95f78b9b4a81b3","sha256:9bfec83816d3b4d9154834ef78efab1457340d630b18f510f03bc5734afbbc4e"],"state_sha256":"840deca5e75eff18b2fbb5542b575f63393ea39c802a75c03fe53c480db4cfc6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GopsWYHFtwit3iE/qKfAWKWhsQPWSEZ1yUlfohiwj8rYkS0i5PVxkVPwUfrf1dG2SKGNNJ5VAo0Gms8mmo41Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T06:01:31.492412Z","bundle_sha256":"4072dc7375f67677bd599338f4516fe73aa828dc7e4d4ebbb1fb446dd2ca6423"}}