{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:VZMUPLJFZBEWKM5UDLKS376PDP","short_pith_number":"pith:VZMUPLJF","canonical_record":{"source":{"id":"1109.4253","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-09-20T09:26:56Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"c12ccc2b52bff81101ee994cb0aa4f641b51461b1ab6f72cde90f3b02f487f66","abstract_canon_sha256":"e90836ee0ed95e89ab895baf0f334be0f447b67d17c5bbeda7d68926dc350bd6"},"schema_version":"1.0"},"canonical_sha256":"ae5947ad25c8496533b41ad52dffcf1bceceda007890072c039c54afe9411ade","source":{"kind":"arxiv","id":"1109.4253","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.4253","created_at":"2026-05-18T02:41:18Z"},{"alias_kind":"arxiv_version","alias_value":"1109.4253v2","created_at":"2026-05-18T02:41:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4253","created_at":"2026-05-18T02:41:18Z"},{"alias_kind":"pith_short_12","alias_value":"VZMUPLJFZBEW","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VZMUPLJFZBEWKM5U","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VZMUPLJF","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:VZMUPLJFZBEWKM5UDLKS376PDP","target":"record","payload":{"canonical_record":{"source":{"id":"1109.4253","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-09-20T09:26:56Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"c12ccc2b52bff81101ee994cb0aa4f641b51461b1ab6f72cde90f3b02f487f66","abstract_canon_sha256":"e90836ee0ed95e89ab895baf0f334be0f447b67d17c5bbeda7d68926dc350bd6"},"schema_version":"1.0"},"canonical_sha256":"ae5947ad25c8496533b41ad52dffcf1bceceda007890072c039c54afe9411ade","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:18.996886Z","signature_b64":"PU2gTu9vJA44FMFzhlItY4ZZJTC0CxoFIlxf2IC5A4ykuIkc3JveYYZKQp9ynwmms5sjp8MqUqtmAHk5IR1EDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae5947ad25c8496533b41ad52dffcf1bceceda007890072c039c54afe9411ade","last_reissued_at":"2026-05-18T02:41:18.996071Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:18.996071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.4253","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":"2026-05-18T02:41:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+U+0/SrQCL8AUdnJBhXHKB1evk9CAoQUM2iUaUmHdSoa3ybDD+SCTDsSxLwyOWhWkiEPtMjO9Cg1wSy+qK0uDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T07:52:49.820362Z"},"content_sha256":"d2abddd6080a977631cc35c84d25ce826969fd81164c0b66459b9b2e98735c89","schema_version":"1.0","event_id":"sha256:d2abddd6080a977631cc35c84d25ce826969fd81164c0b66459b9b2e98735c89"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:VZMUPLJFZBEWKM5UDLKS376PDP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Contact geometry and isosystolic inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SG","authors_text":"Florent Balacheff, Juan-Carlos Alvarez Paiva","submitted_at":"2011-09-20T09:26:56Z","abstract_excerpt":"A long-standing open problem in systolic geometry asks whether a Riemannian metric on the real projective space whose volume equals that of the canonical metric, but is not isometric to it, must necessarily carry a periodic geodesic of length smaller than \\pi. A contact-geometric reformulation of systolic geometry and the use of canonical perturbation theory allow us to solve a parametric version of this problem. Namely, we show that if g_s is a smooth volume-preserving deformation of the canonical metric and at s=0 the deformation is not tangent to all orders to trivial deformations (i.e., to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4253","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":"2026-05-18T02:41:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vGZYvlqt/leb0cC5sxhrYkyjhq3fOakSkldnu74BVQW1uXlIp/2W3+mcFGR0+40d0ONdUpqBtkl9i79tCt/8Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T07:52:49.820956Z"},"content_sha256":"ed658890be99718f4c2d09655115fd795728747c795332b2b004c4f72df2bc6a","schema_version":"1.0","event_id":"sha256:ed658890be99718f4c2d09655115fd795728747c795332b2b004c4f72df2bc6a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VZMUPLJFZBEWKM5UDLKS376PDP/bundle.json","state_url":"https://pith.science/pith/VZMUPLJFZBEWKM5UDLKS376PDP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VZMUPLJFZBEWKM5UDLKS376PDP/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":"2026-07-01T07:52:49Z","links":{"resolver":"https://pith.science/pith/VZMUPLJFZBEWKM5UDLKS376PDP","bundle":"https://pith.science/pith/VZMUPLJFZBEWKM5UDLKS376PDP/bundle.json","state":"https://pith.science/pith/VZMUPLJFZBEWKM5UDLKS376PDP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VZMUPLJFZBEWKM5UDLKS376PDP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:VZMUPLJFZBEWKM5UDLKS376PDP","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":"e90836ee0ed95e89ab895baf0f334be0f447b67d17c5bbeda7d68926dc350bd6","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-09-20T09:26:56Z","title_canon_sha256":"c12ccc2b52bff81101ee994cb0aa4f641b51461b1ab6f72cde90f3b02f487f66"},"schema_version":"1.0","source":{"id":"1109.4253","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.4253","created_at":"2026-05-18T02:41:18Z"},{"alias_kind":"arxiv_version","alias_value":"1109.4253v2","created_at":"2026-05-18T02:41:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4253","created_at":"2026-05-18T02:41:18Z"},{"alias_kind":"pith_short_12","alias_value":"VZMUPLJFZBEW","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VZMUPLJFZBEWKM5U","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VZMUPLJF","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:ed658890be99718f4c2d09655115fd795728747c795332b2b004c4f72df2bc6a","target":"graph","created_at":"2026-05-18T02:41:18Z","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":"A long-standing open problem in systolic geometry asks whether a Riemannian metric on the real projective space whose volume equals that of the canonical metric, but is not isometric to it, must necessarily carry a periodic geodesic of length smaller than \\pi. A contact-geometric reformulation of systolic geometry and the use of canonical perturbation theory allow us to solve a parametric version of this problem. Namely, we show that if g_s is a smooth volume-preserving deformation of the canonical metric and at s=0 the deformation is not tangent to all orders to trivial deformations (i.e., to","authors_text":"Florent Balacheff, Juan-Carlos Alvarez Paiva","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-09-20T09:26:56Z","title":"Contact geometry and isosystolic inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4253","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:d2abddd6080a977631cc35c84d25ce826969fd81164c0b66459b9b2e98735c89","target":"record","created_at":"2026-05-18T02:41:18Z","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":"e90836ee0ed95e89ab895baf0f334be0f447b67d17c5bbeda7d68926dc350bd6","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-09-20T09:26:56Z","title_canon_sha256":"c12ccc2b52bff81101ee994cb0aa4f641b51461b1ab6f72cde90f3b02f487f66"},"schema_version":"1.0","source":{"id":"1109.4253","kind":"arxiv","version":2}},"canonical_sha256":"ae5947ad25c8496533b41ad52dffcf1bceceda007890072c039c54afe9411ade","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae5947ad25c8496533b41ad52dffcf1bceceda007890072c039c54afe9411ade","first_computed_at":"2026-05-18T02:41:18.996071Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:18.996071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PU2gTu9vJA44FMFzhlItY4ZZJTC0CxoFIlxf2IC5A4ykuIkc3JveYYZKQp9ynwmms5sjp8MqUqtmAHk5IR1EDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:18.996886Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.4253","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d2abddd6080a977631cc35c84d25ce826969fd81164c0b66459b9b2e98735c89","sha256:ed658890be99718f4c2d09655115fd795728747c795332b2b004c4f72df2bc6a"],"state_sha256":"85c771e736c27d473552dac006605aed3d7dc3b6ef697ba677359555fcf6eeec"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/FmcXI0/z50YgZQOS7DQEMH3rxEpJv6ZlvsUb5iyrIrbtowXiAX0OfbmFpp9nokZx/ExgRZMIHPsKBWsOrNvAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T07:52:49.824363Z","bundle_sha256":"c1592b62956e07a6021730033bf62bf1d38ec73bd57f13fe8c1b7f5bf84f400a"}}