{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:7Z6HM5XXCFTUNHUQ3GTDFXZJJW","short_pith_number":"pith:7Z6HM5XX","canonical_record":{"source":{"id":"2512.01937","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SG","submitted_at":"2025-12-01T17:50:46Z","cross_cats_sorted":[],"title_canon_sha256":"00b75beb48b776ba897d37b36b1ff51cd8668caad82bdd1544bc2fd2482f416e","abstract_canon_sha256":"77cd9b8139cb331a735251af51829d03d9c80cf2f540e0956ca827d1197b50d6"},"schema_version":"1.0"},"canonical_sha256":"fe7c7676f71167469e90d9a632df294dbf102d46473bf6ecd7a70a5076e179dc","source":{"kind":"arxiv","id":"2512.01937","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.01937","created_at":"2026-05-26T02:05:04Z"},{"alias_kind":"arxiv_version","alias_value":"2512.01937v3","created_at":"2026-05-26T02:05:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.01937","created_at":"2026-05-26T02:05:04Z"},{"alias_kind":"pith_short_12","alias_value":"7Z6HM5XXCFTU","created_at":"2026-05-26T02:05:04Z"},{"alias_kind":"pith_short_16","alias_value":"7Z6HM5XXCFTUNHUQ","created_at":"2026-05-26T02:05:04Z"},{"alias_kind":"pith_short_8","alias_value":"7Z6HM5XX","created_at":"2026-05-26T02:05:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:7Z6HM5XXCFTUNHUQ3GTDFXZJJW","target":"record","payload":{"canonical_record":{"source":{"id":"2512.01937","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SG","submitted_at":"2025-12-01T17:50:46Z","cross_cats_sorted":[],"title_canon_sha256":"00b75beb48b776ba897d37b36b1ff51cd8668caad82bdd1544bc2fd2482f416e","abstract_canon_sha256":"77cd9b8139cb331a735251af51829d03d9c80cf2f540e0956ca827d1197b50d6"},"schema_version":"1.0"},"canonical_sha256":"fe7c7676f71167469e90d9a632df294dbf102d46473bf6ecd7a70a5076e179dc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T02:05:04.293599Z","signature_b64":"PZpWyWF3lVqe2Qt/JkAfHu2zli2S+LTQzeFluQaqsGJnI+qiekx+C+Te2eEEY+EPv7+K9SzfxO4f0Q/a1ljHDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe7c7676f71167469e90d9a632df294dbf102d46473bf6ecd7a70a5076e179dc","last_reissued_at":"2026-05-26T02:05:04.292611Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T02:05:04.292611Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2512.01937","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-26T02:05:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qp47XKHHB2t4Dg9ZAnSlwlmSRqAHfPaXzCnPj+/oDTwRwMlGJuocesoK7YkE20kzrVn9hiKR8DW7USPLjbTuDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T04:05:35.077192Z"},"content_sha256":"e524370fbd818e07a09e0fe542ab652abfea5a45eee2e6e56ee0c8843253bc29","schema_version":"1.0","event_id":"sha256:e524370fbd818e07a09e0fe542ab652abfea5a45eee2e6e56ee0c8843253bc29"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:7Z6HM5XXCFTUNHUQ3GTDFXZJJW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the $C^2$-local systolic optimality of Zoll odd-symplectic forms","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Samanyu Sanjay","submitted_at":"2025-12-01T17:50:46Z","abstract_excerpt":"An odd-symplectic form is a closed and maximally non-degenerate $2$-form on a compact odd-dimensional manifold. It describes the dynamics of an autonomous Hamiltonian system on a regular energy level. It is called Zoll if the induced dynamics is a free circle action, up to a global time reparameterization. This article establishes a normal form theorem for odd-symplectic forms close to a Zoll one and cohomologous to it, which is then used to prove that Zoll odd-symplectic forms are the local maximizers of the associated systolic ratio. This generalizes the known systolic optimality of Zoll con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.01937","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2512.01937/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-05-26T02:05:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gwILIr/pqHa1oyUi0XK8Fwu/j6R3u5HM4WWrqkY1EXhnt5nI8AHnmm+LpFjv+yMmLnQ9aGKXDe/grcJjbmmnCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T04:05:35.077835Z"},"content_sha256":"0f9f40823cd53e1131de729f7380b0efe1a4e699626bebb58b8bd141c3b75013","schema_version":"1.0","event_id":"sha256:0f9f40823cd53e1131de729f7380b0efe1a4e699626bebb58b8bd141c3b75013"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7Z6HM5XXCFTUNHUQ3GTDFXZJJW/bundle.json","state_url":"https://pith.science/pith/7Z6HM5XXCFTUNHUQ3GTDFXZJJW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7Z6HM5XXCFTUNHUQ3GTDFXZJJW/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":"2026-06-11T04:05:35Z","links":{"resolver":"https://pith.science/pith/7Z6HM5XXCFTUNHUQ3GTDFXZJJW","bundle":"https://pith.science/pith/7Z6HM5XXCFTUNHUQ3GTDFXZJJW/bundle.json","state":"https://pith.science/pith/7Z6HM5XXCFTUNHUQ3GTDFXZJJW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7Z6HM5XXCFTUNHUQ3GTDFXZJJW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:7Z6HM5XXCFTUNHUQ3GTDFXZJJW","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":"77cd9b8139cb331a735251af51829d03d9c80cf2f540e0956ca827d1197b50d6","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SG","submitted_at":"2025-12-01T17:50:46Z","title_canon_sha256":"00b75beb48b776ba897d37b36b1ff51cd8668caad82bdd1544bc2fd2482f416e"},"schema_version":"1.0","source":{"id":"2512.01937","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.01937","created_at":"2026-05-26T02:05:04Z"},{"alias_kind":"arxiv_version","alias_value":"2512.01937v3","created_at":"2026-05-26T02:05:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.01937","created_at":"2026-05-26T02:05:04Z"},{"alias_kind":"pith_short_12","alias_value":"7Z6HM5XXCFTU","created_at":"2026-05-26T02:05:04Z"},{"alias_kind":"pith_short_16","alias_value":"7Z6HM5XXCFTUNHUQ","created_at":"2026-05-26T02:05:04Z"},{"alias_kind":"pith_short_8","alias_value":"7Z6HM5XX","created_at":"2026-05-26T02:05:04Z"}],"graph_snapshots":[{"event_id":"sha256:0f9f40823cd53e1131de729f7380b0efe1a4e699626bebb58b8bd141c3b75013","target":"graph","created_at":"2026-05-26T02:05:04Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2512.01937/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"An odd-symplectic form is a closed and maximally non-degenerate $2$-form on a compact odd-dimensional manifold. It describes the dynamics of an autonomous Hamiltonian system on a regular energy level. It is called Zoll if the induced dynamics is a free circle action, up to a global time reparameterization. This article establishes a normal form theorem for odd-symplectic forms close to a Zoll one and cohomologous to it, which is then used to prove that Zoll odd-symplectic forms are the local maximizers of the associated systolic ratio. This generalizes the known systolic optimality of Zoll con","authors_text":"Samanyu Sanjay","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SG","submitted_at":"2025-12-01T17:50:46Z","title":"On the $C^2$-local systolic optimality of Zoll odd-symplectic forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.01937","kind":"arxiv","version":3},"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:e524370fbd818e07a09e0fe542ab652abfea5a45eee2e6e56ee0c8843253bc29","target":"record","created_at":"2026-05-26T02:05:04Z","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":"77cd9b8139cb331a735251af51829d03d9c80cf2f540e0956ca827d1197b50d6","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SG","submitted_at":"2025-12-01T17:50:46Z","title_canon_sha256":"00b75beb48b776ba897d37b36b1ff51cd8668caad82bdd1544bc2fd2482f416e"},"schema_version":"1.0","source":{"id":"2512.01937","kind":"arxiv","version":3}},"canonical_sha256":"fe7c7676f71167469e90d9a632df294dbf102d46473bf6ecd7a70a5076e179dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe7c7676f71167469e90d9a632df294dbf102d46473bf6ecd7a70a5076e179dc","first_computed_at":"2026-05-26T02:05:04.292611Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T02:05:04.292611Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PZpWyWF3lVqe2Qt/JkAfHu2zli2S+LTQzeFluQaqsGJnI+qiekx+C+Te2eEEY+EPv7+K9SzfxO4f0Q/a1ljHDg==","signature_status":"signed_v1","signed_at":"2026-05-26T02:05:04.293599Z","signed_message":"canonical_sha256_bytes"},"source_id":"2512.01937","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e524370fbd818e07a09e0fe542ab652abfea5a45eee2e6e56ee0c8843253bc29","sha256:0f9f40823cd53e1131de729f7380b0efe1a4e699626bebb58b8bd141c3b75013"],"state_sha256":"3cc864d1b06aae52579f81f41a8ea43de2c2233010430ed28ae7268bfc9de042"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w7taP3y5Hb9Un9HF11aSXOFLu01jLuyLy9hwJciyR0ig60/qvuVwOamy800tPZ2ytaab+7bUJmjxWXQ+i9cLCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T04:05:35.081506Z","bundle_sha256":"3d468b63d119d6e94a2253732476f958cc5ef97be15f6d778df7484ce640b7cd"}}