{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:ZQA6IPU64NZOQJ63O3OTTGU3GW","short_pith_number":"pith:ZQA6IPU6","canonical_record":{"source":{"id":"1703.03725","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-03-10T15:46:57Z","cross_cats_sorted":[],"title_canon_sha256":"3411736ee78ab47ad2989e4ec0b6ed3cc6ec72f298c62dacfa43f3ecf952e2eb","abstract_canon_sha256":"13916e60d83f88175017b9527a7905a2f52531e9f275bc7dbd0e2cf7268bb4f0"},"schema_version":"1.0"},"canonical_sha256":"cc01e43e9ee372e827db76dd399a9b35843e59855fa6bc6894edaaf6fc6a49f3","source":{"kind":"arxiv","id":"1703.03725","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.03725","created_at":"2026-05-18T00:48:55Z"},{"alias_kind":"arxiv_version","alias_value":"1703.03725v1","created_at":"2026-05-18T00:48:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.03725","created_at":"2026-05-18T00:48:55Z"},{"alias_kind":"pith_short_12","alias_value":"ZQA6IPU64NZO","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZQA6IPU64NZOQJ63","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZQA6IPU6","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:ZQA6IPU64NZOQJ63O3OTTGU3GW","target":"record","payload":{"canonical_record":{"source":{"id":"1703.03725","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-03-10T15:46:57Z","cross_cats_sorted":[],"title_canon_sha256":"3411736ee78ab47ad2989e4ec0b6ed3cc6ec72f298c62dacfa43f3ecf952e2eb","abstract_canon_sha256":"13916e60d83f88175017b9527a7905a2f52531e9f275bc7dbd0e2cf7268bb4f0"},"schema_version":"1.0"},"canonical_sha256":"cc01e43e9ee372e827db76dd399a9b35843e59855fa6bc6894edaaf6fc6a49f3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:55.973765Z","signature_b64":"Xr/w9aTDJX2N6YVT4H1imMCZqe8Fd1OG/YWHkafHAi8cs+J1lYED7Lf1fvlU2ujuO1DCCoV/bAoyY9RQ7VavCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc01e43e9ee372e827db76dd399a9b35843e59855fa6bc6894edaaf6fc6a49f3","last_reissued_at":"2026-05-18T00:48:55.973104Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:55.973104Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.03725","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":"2026-05-18T00:48:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"36czqs2wSrScuO/IErRIrjtb3t1wQNRt4EpY0pEWOU88fYOaKVy6KvsNTLF2gkAU+sxjP6Y6XRFtVVJXtYyRCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:40:23.771425Z"},"content_sha256":"3097d7dea063f98f17cf4b1eac1c54d98e6b0c21428acdba67114f9b2eb717d3","schema_version":"1.0","event_id":"sha256:3097d7dea063f98f17cf4b1eac1c54d98e6b0c21428acdba67114f9b2eb717d3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:ZQA6IPU64NZOQJ63O3OTTGU3GW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rank of ordinary webs in codimension one. An effective method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Daniel Lehmann, Jean Paul Dufour","submitted_at":"2017-03-10T15:46:57Z","abstract_excerpt":"We are interested by holomorphic $d$-webs $W$ of codimension one in a complex $n$-dimensional manifold $M$. If they are ordinary, i.e. if they satisfy to some condition of genericity (whose precise definition is recalled), we proved in [CL] that their rank $\\rho(W)$ is upper-bounded by a certain number $\\pi'(n,d)\\ \\bigl($which, for $n\\geq 3$, is stictly smaller than the Castelnuovo-Chern's bound $\\pi(n,d)\\bigr)$. In fact, denoting by $c(n,h)$ the dimension of the space of homogeneous polynomials of degree $h$ with $n$ unknowns, and by $h_0$ the integer such that $$c(n,h_0-1)<d\\leq c(n,h_0),$$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03725","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":"2026-05-18T00:48:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hf+RluMUAN7nq2GxiWsogihHBF/0JCX8JF/MhSuWXYFQuaiid+hVMl76NkHfYo28RUbInz6mxL5aj8ac6E6MAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:40:23.772052Z"},"content_sha256":"c68dc8ed6a8b25300165a2fa02e6d041ebd42af03932b7b4d7af259a01992609","schema_version":"1.0","event_id":"sha256:c68dc8ed6a8b25300165a2fa02e6d041ebd42af03932b7b4d7af259a01992609"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZQA6IPU64NZOQJ63O3OTTGU3GW/bundle.json","state_url":"https://pith.science/pith/ZQA6IPU64NZOQJ63O3OTTGU3GW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZQA6IPU64NZOQJ63O3OTTGU3GW/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":"2026-05-28T22:40:23Z","links":{"resolver":"https://pith.science/pith/ZQA6IPU64NZOQJ63O3OTTGU3GW","bundle":"https://pith.science/pith/ZQA6IPU64NZOQJ63O3OTTGU3GW/bundle.json","state":"https://pith.science/pith/ZQA6IPU64NZOQJ63O3OTTGU3GW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZQA6IPU64NZOQJ63O3OTTGU3GW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZQA6IPU64NZOQJ63O3OTTGU3GW","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":"13916e60d83f88175017b9527a7905a2f52531e9f275bc7dbd0e2cf7268bb4f0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-03-10T15:46:57Z","title_canon_sha256":"3411736ee78ab47ad2989e4ec0b6ed3cc6ec72f298c62dacfa43f3ecf952e2eb"},"schema_version":"1.0","source":{"id":"1703.03725","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.03725","created_at":"2026-05-18T00:48:55Z"},{"alias_kind":"arxiv_version","alias_value":"1703.03725v1","created_at":"2026-05-18T00:48:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.03725","created_at":"2026-05-18T00:48:55Z"},{"alias_kind":"pith_short_12","alias_value":"ZQA6IPU64NZO","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZQA6IPU64NZOQJ63","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZQA6IPU6","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:c68dc8ed6a8b25300165a2fa02e6d041ebd42af03932b7b4d7af259a01992609","target":"graph","created_at":"2026-05-18T00:48:55Z","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 are interested by holomorphic $d$-webs $W$ of codimension one in a complex $n$-dimensional manifold $M$. If they are ordinary, i.e. if they satisfy to some condition of genericity (whose precise definition is recalled), we proved in [CL] that their rank $\\rho(W)$ is upper-bounded by a certain number $\\pi'(n,d)\\ \\bigl($which, for $n\\geq 3$, is stictly smaller than the Castelnuovo-Chern's bound $\\pi(n,d)\\bigr)$. In fact, denoting by $c(n,h)$ the dimension of the space of homogeneous polynomials of degree $h$ with $n$ unknowns, and by $h_0$ the integer such that $$c(n,h_0-1)<d\\leq c(n,h_0),$$ ","authors_text":"Daniel Lehmann, Jean Paul Dufour","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-03-10T15:46:57Z","title":"Rank of ordinary webs in codimension one. An effective method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03725","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":"sha256:3097d7dea063f98f17cf4b1eac1c54d98e6b0c21428acdba67114f9b2eb717d3","target":"record","created_at":"2026-05-18T00:48:55Z","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":"13916e60d83f88175017b9527a7905a2f52531e9f275bc7dbd0e2cf7268bb4f0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-03-10T15:46:57Z","title_canon_sha256":"3411736ee78ab47ad2989e4ec0b6ed3cc6ec72f298c62dacfa43f3ecf952e2eb"},"schema_version":"1.0","source":{"id":"1703.03725","kind":"arxiv","version":1}},"canonical_sha256":"cc01e43e9ee372e827db76dd399a9b35843e59855fa6bc6894edaaf6fc6a49f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc01e43e9ee372e827db76dd399a9b35843e59855fa6bc6894edaaf6fc6a49f3","first_computed_at":"2026-05-18T00:48:55.973104Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:55.973104Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Xr/w9aTDJX2N6YVT4H1imMCZqe8Fd1OG/YWHkafHAi8cs+J1lYED7Lf1fvlU2ujuO1DCCoV/bAoyY9RQ7VavCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:55.973765Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.03725","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3097d7dea063f98f17cf4b1eac1c54d98e6b0c21428acdba67114f9b2eb717d3","sha256:c68dc8ed6a8b25300165a2fa02e6d041ebd42af03932b7b4d7af259a01992609"],"state_sha256":"9dcf61a4a100349ee059af2ca4323bac9017df124517d076cc7164ab2f3aa7ea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1LbhDixAsMqzCspjGbI4oeEV3x/OBzqAH1iohom0QesL2vu6OJxk87ppVdRT1wQ9fwp3Mh73rGAgEvbKJnivCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T22:40:23.775776Z","bundle_sha256":"cb3093b12509ef1872b31b57784f6c501c26e64373b94f9feec88777a14fca84"}}