{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:RW5BSHZFETCNFUXU7NRYBPLYVJ","short_pith_number":"pith:RW5BSHZF","canonical_record":{"source":{"id":"1105.3888","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-05-19T14:39:25Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"2f73947d64f0fa815965da233648ee05ef80125e3b65ef16a8591d32f9bb0676","abstract_canon_sha256":"627e3545faae0e49c321234dd014ff64e23afa8e3fb39c268732219712ed8700"},"schema_version":"1.0"},"canonical_sha256":"8dba191f2524c4d2d2f4fb6380bd78aa7818ebfbcbef0ae02c4da7e129d3fc64","source":{"kind":"arxiv","id":"1105.3888","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.3888","created_at":"2026-05-18T03:07:21Z"},{"alias_kind":"arxiv_version","alias_value":"1105.3888v1","created_at":"2026-05-18T03:07:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.3888","created_at":"2026-05-18T03:07:21Z"},{"alias_kind":"pith_short_12","alias_value":"RW5BSHZFETCN","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RW5BSHZFETCNFUXU","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RW5BSHZF","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:RW5BSHZFETCNFUXU7NRYBPLYVJ","target":"record","payload":{"canonical_record":{"source":{"id":"1105.3888","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-05-19T14:39:25Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"2f73947d64f0fa815965da233648ee05ef80125e3b65ef16a8591d32f9bb0676","abstract_canon_sha256":"627e3545faae0e49c321234dd014ff64e23afa8e3fb39c268732219712ed8700"},"schema_version":"1.0"},"canonical_sha256":"8dba191f2524c4d2d2f4fb6380bd78aa7818ebfbcbef0ae02c4da7e129d3fc64","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:21.143273Z","signature_b64":"6uwHbjgQ4rKjxC8hNqR0vphJrmIngRnV5zhrYo9sjgud+CP2Hv58Xy1P77MH/bkdrhihWe5tRRyn4VZCFKdYCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8dba191f2524c4d2d2f4fb6380bd78aa7818ebfbcbef0ae02c4da7e129d3fc64","last_reissued_at":"2026-05-18T03:07:21.142618Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:21.142618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.3888","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":"2026-05-18T03:07:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k48PieyX86Xz/bxAVRF/DGsStWuSxC7b9DtGBUiW4bJ0FXzxjunRrVJATcR9TVM8WVoTb3fbfwc0BL9f/2BlCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:35:33.179757Z"},"content_sha256":"ad9a741221fd912e8b93905cb6ae4726b4f884d485c9cd34e6236fad4cc23b7b","schema_version":"1.0","event_id":"sha256:ad9a741221fd912e8b93905cb6ae4726b4f884d485c9cd34e6236fad4cc23b7b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:RW5BSHZFETCNFUXU7NRYBPLYVJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On restricted Analytic Gradients on Analytic Isolated Surface Singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CA","authors_text":"Fernando Sanz, Vincent Grandjean","submitted_at":"2011-05-19T14:39:25Z","abstract_excerpt":"Let (X,O) be a real analytic isolated surface singularity at the origin o of a real analytic manifold M equipped with a real analytic metric g. Given a real analytic function f:(M,O) --> (R,0) singular at O, we prove that the gradient trajectories for the metric g|(X,O) of the restriction f|X escaping from or ending up at the origin O do not oscillate. Such a trajectory is thus a sub-pfaffian set. Moreover, in each connected component of X\\O where the restricted gradient does not vanish, there is always a trajectory accumulating at O and admitting a formal asymptotic expansion at O"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3888","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":"2026-05-18T03:07:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cyAN3Wm8WZxtFLYMsl6PXY0jC8+kE1Bns7c4KYOLglwN+5Cz32qVO5jM/wfPulslZ+Jv4kXEse/8JlZmnwd+Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:35:33.180111Z"},"content_sha256":"db7ba91f2c4c72d7f968b6972411635cd563089f1b24a1d9a05207aff1debf75","schema_version":"1.0","event_id":"sha256:db7ba91f2c4c72d7f968b6972411635cd563089f1b24a1d9a05207aff1debf75"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RW5BSHZFETCNFUXU7NRYBPLYVJ/bundle.json","state_url":"https://pith.science/pith/RW5BSHZFETCNFUXU7NRYBPLYVJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RW5BSHZFETCNFUXU7NRYBPLYVJ/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":"2026-05-30T08:35:33Z","links":{"resolver":"https://pith.science/pith/RW5BSHZFETCNFUXU7NRYBPLYVJ","bundle":"https://pith.science/pith/RW5BSHZFETCNFUXU7NRYBPLYVJ/bundle.json","state":"https://pith.science/pith/RW5BSHZFETCNFUXU7NRYBPLYVJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RW5BSHZFETCNFUXU7NRYBPLYVJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:RW5BSHZFETCNFUXU7NRYBPLYVJ","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":"627e3545faae0e49c321234dd014ff64e23afa8e3fb39c268732219712ed8700","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-05-19T14:39:25Z","title_canon_sha256":"2f73947d64f0fa815965da233648ee05ef80125e3b65ef16a8591d32f9bb0676"},"schema_version":"1.0","source":{"id":"1105.3888","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.3888","created_at":"2026-05-18T03:07:21Z"},{"alias_kind":"arxiv_version","alias_value":"1105.3888v1","created_at":"2026-05-18T03:07:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.3888","created_at":"2026-05-18T03:07:21Z"},{"alias_kind":"pith_short_12","alias_value":"RW5BSHZFETCN","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RW5BSHZFETCNFUXU","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RW5BSHZF","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:db7ba91f2c4c72d7f968b6972411635cd563089f1b24a1d9a05207aff1debf75","target":"graph","created_at":"2026-05-18T03:07:21Z","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":"Let (X,O) be a real analytic isolated surface singularity at the origin o of a real analytic manifold M equipped with a real analytic metric g. Given a real analytic function f:(M,O) --> (R,0) singular at O, we prove that the gradient trajectories for the metric g|(X,O) of the restriction f|X escaping from or ending up at the origin O do not oscillate. Such a trajectory is thus a sub-pfaffian set. Moreover, in each connected component of X\\O where the restricted gradient does not vanish, there is always a trajectory accumulating at O and admitting a formal asymptotic expansion at O","authors_text":"Fernando Sanz, Vincent Grandjean","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-05-19T14:39:25Z","title":"On restricted Analytic Gradients on Analytic Isolated Surface Singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3888","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:ad9a741221fd912e8b93905cb6ae4726b4f884d485c9cd34e6236fad4cc23b7b","target":"record","created_at":"2026-05-18T03:07:21Z","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":"627e3545faae0e49c321234dd014ff64e23afa8e3fb39c268732219712ed8700","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-05-19T14:39:25Z","title_canon_sha256":"2f73947d64f0fa815965da233648ee05ef80125e3b65ef16a8591d32f9bb0676"},"schema_version":"1.0","source":{"id":"1105.3888","kind":"arxiv","version":1}},"canonical_sha256":"8dba191f2524c4d2d2f4fb6380bd78aa7818ebfbcbef0ae02c4da7e129d3fc64","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8dba191f2524c4d2d2f4fb6380bd78aa7818ebfbcbef0ae02c4da7e129d3fc64","first_computed_at":"2026-05-18T03:07:21.142618Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:21.142618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6uwHbjgQ4rKjxC8hNqR0vphJrmIngRnV5zhrYo9sjgud+CP2Hv58Xy1P77MH/bkdrhihWe5tRRyn4VZCFKdYCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:21.143273Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.3888","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad9a741221fd912e8b93905cb6ae4726b4f884d485c9cd34e6236fad4cc23b7b","sha256:db7ba91f2c4c72d7f968b6972411635cd563089f1b24a1d9a05207aff1debf75"],"state_sha256":"0b8b1b3e87a7c79d3eb4b800fb8197d5631404a1340dded5b5e1bc208857469f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NPp6bE2bt0J/UAn0JcnV/BDTB0ZCa6xjZnQ/tGsV/90RTGaFiT5ugKT6lmOAthekU9I1zvloz/KPt7W5rmXQAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T08:35:33.182008Z","bundle_sha256":"7020efcaffc71f1517f28cdb24ef978016ad6fb7c9d240a9b846b5c15452ba39"}}