{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ZGCD6FUEEXGZFC2BQWW5WXGL3Y","short_pith_number":"pith:ZGCD6FUE","canonical_record":{"source":{"id":"1307.7290","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-07-27T18:18:56Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"6ed005c99124cb2e089605705982cc7afa233f22b1c404f82f1963b4c4c4a18b","abstract_canon_sha256":"5d8956158148e14fc66a343adbc763b1a5e750a88c17ba4e824a98c76908a9c1"},"schema_version":"1.0"},"canonical_sha256":"c9843f168425cd928b4185addb5ccbde3518f1d5a3bbea43d924814889bfaa2b","source":{"kind":"arxiv","id":"1307.7290","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.7290","created_at":"2026-05-18T03:17:23Z"},{"alias_kind":"arxiv_version","alias_value":"1307.7290v1","created_at":"2026-05-18T03:17:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.7290","created_at":"2026-05-18T03:17:23Z"},{"alias_kind":"pith_short_12","alias_value":"ZGCD6FUEEXGZ","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZGCD6FUEEXGZFC2B","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZGCD6FUE","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ZGCD6FUEEXGZFC2BQWW5WXGL3Y","target":"record","payload":{"canonical_record":{"source":{"id":"1307.7290","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-07-27T18:18:56Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"6ed005c99124cb2e089605705982cc7afa233f22b1c404f82f1963b4c4c4a18b","abstract_canon_sha256":"5d8956158148e14fc66a343adbc763b1a5e750a88c17ba4e824a98c76908a9c1"},"schema_version":"1.0"},"canonical_sha256":"c9843f168425cd928b4185addb5ccbde3518f1d5a3bbea43d924814889bfaa2b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:23.703656Z","signature_b64":"qatlop762twZVA4qVEI7zkxHrhSx/QesluphCtBz/zjr0hTapfeyMhSwwBnymRNq72AFCclABMiSPynEPNvtDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9843f168425cd928b4185addb5ccbde3518f1d5a3bbea43d924814889bfaa2b","last_reissued_at":"2026-05-18T03:17:23.702930Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:23.702930Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.7290","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:17:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J4+wdsyfi8M7eHUlvtiXHvLBigJme4QqX7BCtqVNob7rGhxpRsemIZ896dXtp3p/qMRu1IsyLLWx6Rl6F5HQBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T00:53:44.930904Z"},"content_sha256":"caa036f0b9157a04c67210cc29e32d91147b7e04c56e0970b09e7dbbc2811907","schema_version":"1.0","event_id":"sha256:caa036f0b9157a04c67210cc29e32d91147b7e04c56e0970b09e7dbbc2811907"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ZGCD6FUEEXGZFC2BQWW5WXGL3Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Slow volume growth for Reeb flows on spherizations and contact Bott--Samelson theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.DS","authors_text":"Cl\\'emence Labrousse, Felix Schlenk, Urs Frauenfelder","submitted_at":"2013-07-27T18:18:56Z","abstract_excerpt":"We give a uniform lower bound for the polynomial complexity of all Reeb flows on the spherization (S*M,\\xi) over a closed manifold. Our measure for the dynamical complexity of Reeb flows is slow volume growth, a polynomial version of topological entropy, and our uniform bound is in terms of the polynomial growth of the homology of the based loops space of M. As an application, we extend the Bott--Samelson theorem from geodesic flows to Reeb flows: If (S*M,\\xi) admits a periodic Reeb flow, or, more generally, if there exists a positive Legendrian loop of a fibre S*_q M, then M is a circle or th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7290","kind":"arxiv","version":1},"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":"2026-05-18T03:17:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bi30KmD05AYzAI3HJ0rdWKZDg3SYEyRbnYFveJdMC9xt1UueKh/Ls5hiUAo8lvyOjuY0Zh8n6Ifa9IWp1TXJDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T00:53:44.931245Z"},"content_sha256":"d93e03e638878e96fba183b8134ea5763375b79157044936dc876817df228e1d","schema_version":"1.0","event_id":"sha256:d93e03e638878e96fba183b8134ea5763375b79157044936dc876817df228e1d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZGCD6FUEEXGZFC2BQWW5WXGL3Y/bundle.json","state_url":"https://pith.science/pith/ZGCD6FUEEXGZFC2BQWW5WXGL3Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZGCD6FUEEXGZFC2BQWW5WXGL3Y/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":"2026-06-30T00:53:44Z","links":{"resolver":"https://pith.science/pith/ZGCD6FUEEXGZFC2BQWW5WXGL3Y","bundle":"https://pith.science/pith/ZGCD6FUEEXGZFC2BQWW5WXGL3Y/bundle.json","state":"https://pith.science/pith/ZGCD6FUEEXGZFC2BQWW5WXGL3Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZGCD6FUEEXGZFC2BQWW5WXGL3Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ZGCD6FUEEXGZFC2BQWW5WXGL3Y","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":"5d8956158148e14fc66a343adbc763b1a5e750a88c17ba4e824a98c76908a9c1","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-07-27T18:18:56Z","title_canon_sha256":"6ed005c99124cb2e089605705982cc7afa233f22b1c404f82f1963b4c4c4a18b"},"schema_version":"1.0","source":{"id":"1307.7290","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.7290","created_at":"2026-05-18T03:17:23Z"},{"alias_kind":"arxiv_version","alias_value":"1307.7290v1","created_at":"2026-05-18T03:17:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.7290","created_at":"2026-05-18T03:17:23Z"},{"alias_kind":"pith_short_12","alias_value":"ZGCD6FUEEXGZ","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZGCD6FUEEXGZFC2B","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZGCD6FUE","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:d93e03e638878e96fba183b8134ea5763375b79157044936dc876817df228e1d","target":"graph","created_at":"2026-05-18T03:17:23Z","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 give a uniform lower bound for the polynomial complexity of all Reeb flows on the spherization (S*M,\\xi) over a closed manifold. Our measure for the dynamical complexity of Reeb flows is slow volume growth, a polynomial version of topological entropy, and our uniform bound is in terms of the polynomial growth of the homology of the based loops space of M. As an application, we extend the Bott--Samelson theorem from geodesic flows to Reeb flows: If (S*M,\\xi) admits a periodic Reeb flow, or, more generally, if there exists a positive Legendrian loop of a fibre S*_q M, then M is a circle or th","authors_text":"Cl\\'emence Labrousse, Felix Schlenk, Urs Frauenfelder","cross_cats":["math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-07-27T18:18:56Z","title":"Slow volume growth for Reeb flows on spherizations and contact Bott--Samelson theorems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7290","kind":"arxiv","version":1},"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:caa036f0b9157a04c67210cc29e32d91147b7e04c56e0970b09e7dbbc2811907","target":"record","created_at":"2026-05-18T03:17:23Z","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":"5d8956158148e14fc66a343adbc763b1a5e750a88c17ba4e824a98c76908a9c1","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-07-27T18:18:56Z","title_canon_sha256":"6ed005c99124cb2e089605705982cc7afa233f22b1c404f82f1963b4c4c4a18b"},"schema_version":"1.0","source":{"id":"1307.7290","kind":"arxiv","version":1}},"canonical_sha256":"c9843f168425cd928b4185addb5ccbde3518f1d5a3bbea43d924814889bfaa2b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c9843f168425cd928b4185addb5ccbde3518f1d5a3bbea43d924814889bfaa2b","first_computed_at":"2026-05-18T03:17:23.702930Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:23.702930Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qatlop762twZVA4qVEI7zkxHrhSx/QesluphCtBz/zjr0hTapfeyMhSwwBnymRNq72AFCclABMiSPynEPNvtDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:23.703656Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.7290","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:caa036f0b9157a04c67210cc29e32d91147b7e04c56e0970b09e7dbbc2811907","sha256:d93e03e638878e96fba183b8134ea5763375b79157044936dc876817df228e1d"],"state_sha256":"54d7435875c85fc0d0a0d63b59171d0a99e94c3fe476d17e3e6807fb798bf06f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LdYhh9pKOE6JWCtP2Yh1alF8cW5lmrd+W2nRBBkhVDD6BGv/jLlMW81+v/jbwDAiF1fpAR/iIGT6rC3FP67YAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T00:53:44.933114Z","bundle_sha256":"3f3adeced00189c7b5c88fd2a8eb5ac565de0b6428df2a7a7e147338d213f825"}}