{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:QZLLCZLGI6IDCOD3Y7OMOOLM7X","short_pith_number":"pith:QZLLCZLG","canonical_record":{"source":{"id":"1206.0525","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-06-04T05:59:17Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"03e53fa432f8068d9dfa1357fc00498046af075455c2050371301185e7146a34","abstract_canon_sha256":"e4d7faf3a2ac2f0fc862c21fa8dc00116044b11bd57c05c28fd2fb55f5abadb5"},"schema_version":"1.0"},"canonical_sha256":"8656b16566479031387bc7dcc7396cfdf58929c2872244a8f5327ce90ec64963","source":{"kind":"arxiv","id":"1206.0525","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.0525","created_at":"2026-05-18T00:44:30Z"},{"alias_kind":"arxiv_version","alias_value":"1206.0525v3","created_at":"2026-05-18T00:44:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.0525","created_at":"2026-05-18T00:44:30Z"},{"alias_kind":"pith_short_12","alias_value":"QZLLCZLGI6ID","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"QZLLCZLGI6IDCOD3","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"QZLLCZLG","created_at":"2026-05-18T12:27:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:QZLLCZLGI6IDCOD3Y7OMOOLM7X","target":"record","payload":{"canonical_record":{"source":{"id":"1206.0525","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-06-04T05:59:17Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"03e53fa432f8068d9dfa1357fc00498046af075455c2050371301185e7146a34","abstract_canon_sha256":"e4d7faf3a2ac2f0fc862c21fa8dc00116044b11bd57c05c28fd2fb55f5abadb5"},"schema_version":"1.0"},"canonical_sha256":"8656b16566479031387bc7dcc7396cfdf58929c2872244a8f5327ce90ec64963","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:30.363570Z","signature_b64":"3qRhfV+Oc5f0Ws3dTJFMLdmIvhlowBzR6JOTwRB5fGufMPpVH5BqBV4rwmf73XyqwQVpKwx1ykPhBlBE7GORBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8656b16566479031387bc7dcc7396cfdf58929c2872244a8f5327ce90ec64963","last_reissued_at":"2026-05-18T00:44:30.363087Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:30.363087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.0525","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":"2026-05-18T00:44:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qWhBlbR6he55L52rUIgwDaHbD45a+6g0NkPJHnQZdal7nw8MHQlCQEPNdJdQpL5aZ/FbqZM82OLLkzD9cG8gCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T02:47:25.483588Z"},"content_sha256":"be3eac638c613f9d478b5dbc7b2d10de847bfd67202764191956070d3db52651","schema_version":"1.0","event_id":"sha256:be3eac638c613f9d478b5dbc7b2d10de847bfd67202764191956070d3db52651"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:QZLLCZLGI6IDCOD3Y7OMOOLM7X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A'Campo curvature bumps and the Dirac phenomenon near a singular point","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"L. Paunescu, S. Koike, T-C. Kuo","submitted_at":"2012-06-04T05:59:17Z","abstract_excerpt":"The level curves of an analytic function germ almost always have bumps at unexpected points near the singularity. This profound discovery of N. A'Campo is fully explored in this paper for $f(z,w)\\in \\C\\{z,w\\}$, using the Newton-Puiseux infinitesimals and the notion of gradient canyon. Equally unexpected is the Dirac phenomenon: as $c\\ra 0$, the total Gaussian curvature of $f(z,w)=c$ accumulates in the gradient canyons."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.0525","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":""},"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":"2026-05-18T00:44:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pBb3U3S+KLaomHXNExs8do9hu0w7HLyq7fxyZUfkkBDFFjOug02cogx957uc468DDP3Mu65L/aKvhMgy8UCvAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T02:47:25.484311Z"},"content_sha256":"eb4bffc917ae8db8d4213206edee6652640f393ba4b4d2c8d0936df8b32eb6b5","schema_version":"1.0","event_id":"sha256:eb4bffc917ae8db8d4213206edee6652640f393ba4b4d2c8d0936df8b32eb6b5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QZLLCZLGI6IDCOD3Y7OMOOLM7X/bundle.json","state_url":"https://pith.science/pith/QZLLCZLGI6IDCOD3Y7OMOOLM7X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QZLLCZLGI6IDCOD3Y7OMOOLM7X/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":"2026-06-10T02:47:25Z","links":{"resolver":"https://pith.science/pith/QZLLCZLGI6IDCOD3Y7OMOOLM7X","bundle":"https://pith.science/pith/QZLLCZLGI6IDCOD3Y7OMOOLM7X/bundle.json","state":"https://pith.science/pith/QZLLCZLGI6IDCOD3Y7OMOOLM7X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QZLLCZLGI6IDCOD3Y7OMOOLM7X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QZLLCZLGI6IDCOD3Y7OMOOLM7X","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":"e4d7faf3a2ac2f0fc862c21fa8dc00116044b11bd57c05c28fd2fb55f5abadb5","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-06-04T05:59:17Z","title_canon_sha256":"03e53fa432f8068d9dfa1357fc00498046af075455c2050371301185e7146a34"},"schema_version":"1.0","source":{"id":"1206.0525","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.0525","created_at":"2026-05-18T00:44:30Z"},{"alias_kind":"arxiv_version","alias_value":"1206.0525v3","created_at":"2026-05-18T00:44:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.0525","created_at":"2026-05-18T00:44:30Z"},{"alias_kind":"pith_short_12","alias_value":"QZLLCZLGI6ID","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"QZLLCZLGI6IDCOD3","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"QZLLCZLG","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:eb4bffc917ae8db8d4213206edee6652640f393ba4b4d2c8d0936df8b32eb6b5","target":"graph","created_at":"2026-05-18T00:44:30Z","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":"The level curves of an analytic function germ almost always have bumps at unexpected points near the singularity. This profound discovery of N. A'Campo is fully explored in this paper for $f(z,w)\\in \\C\\{z,w\\}$, using the Newton-Puiseux infinitesimals and the notion of gradient canyon. Equally unexpected is the Dirac phenomenon: as $c\\ra 0$, the total Gaussian curvature of $f(z,w)=c$ accumulates in the gradient canyons.","authors_text":"L. Paunescu, S. Koike, T-C. Kuo","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-06-04T05:59:17Z","title":"A'Campo curvature bumps and the Dirac phenomenon near a singular point"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.0525","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:be3eac638c613f9d478b5dbc7b2d10de847bfd67202764191956070d3db52651","target":"record","created_at":"2026-05-18T00:44:30Z","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":"e4d7faf3a2ac2f0fc862c21fa8dc00116044b11bd57c05c28fd2fb55f5abadb5","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-06-04T05:59:17Z","title_canon_sha256":"03e53fa432f8068d9dfa1357fc00498046af075455c2050371301185e7146a34"},"schema_version":"1.0","source":{"id":"1206.0525","kind":"arxiv","version":3}},"canonical_sha256":"8656b16566479031387bc7dcc7396cfdf58929c2872244a8f5327ce90ec64963","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8656b16566479031387bc7dcc7396cfdf58929c2872244a8f5327ce90ec64963","first_computed_at":"2026-05-18T00:44:30.363087Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:30.363087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3qRhfV+Oc5f0Ws3dTJFMLdmIvhlowBzR6JOTwRB5fGufMPpVH5BqBV4rwmf73XyqwQVpKwx1ykPhBlBE7GORBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:30.363570Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.0525","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be3eac638c613f9d478b5dbc7b2d10de847bfd67202764191956070d3db52651","sha256:eb4bffc917ae8db8d4213206edee6652640f393ba4b4d2c8d0936df8b32eb6b5"],"state_sha256":"7e2fc6d775f82e8bdd49a90be6c833b559d560c486bd66c2be0a2cdbc71ff6db"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IWkF2SPI98Z2fQIsLoo9G/sRfdTmTuV1cget4axYD9Tdklwz09ZLfHAJnA4M+Ye0IrglN/qRpTF3K3NUHU/iCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T02:47:25.488867Z","bundle_sha256":"58edd37391abed6c2be395245576d84966c4d5ce6978795a409c8bdfc53f4e84"}}