{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:3W4WOYLDMCP4WMLLR2S7D3U4EL","short_pith_number":"pith:3W4WOYLD","canonical_record":{"source":{"id":"0707.3404","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2007-07-23T16:01:42Z","cross_cats_sorted":[],"title_canon_sha256":"6eecb2f9902133aeb0e8deadabd2528fcece6c2a4481888708fabdcdf5d442ef","abstract_canon_sha256":"f19d3d66c8bd9d2b358ef2c37432db846829e8df650fd07eec87c43f4e9013fe"},"schema_version":"1.0"},"canonical_sha256":"ddb9676163609fcb316b8ea5f1ee9c22c00d4c1ac5588d4d1244ec38921f8ace","source":{"kind":"arxiv","id":"0707.3404","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0707.3404","created_at":"2026-05-18T03:49:22Z"},{"alias_kind":"arxiv_version","alias_value":"0707.3404v1","created_at":"2026-05-18T03:49:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0707.3404","created_at":"2026-05-18T03:49:22Z"},{"alias_kind":"pith_short_12","alias_value":"3W4WOYLDMCP4","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"3W4WOYLDMCP4WMLL","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"3W4WOYLD","created_at":"2026-05-18T12:25:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:3W4WOYLDMCP4WMLLR2S7D3U4EL","target":"record","payload":{"canonical_record":{"source":{"id":"0707.3404","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2007-07-23T16:01:42Z","cross_cats_sorted":[],"title_canon_sha256":"6eecb2f9902133aeb0e8deadabd2528fcece6c2a4481888708fabdcdf5d442ef","abstract_canon_sha256":"f19d3d66c8bd9d2b358ef2c37432db846829e8df650fd07eec87c43f4e9013fe"},"schema_version":"1.0"},"canonical_sha256":"ddb9676163609fcb316b8ea5f1ee9c22c00d4c1ac5588d4d1244ec38921f8ace","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:49:22.705008Z","signature_b64":"WFsseiEW8zfZNtY6NObfFw89orMUxupq7zM7ZeyvWDS/kI5iFCfJnL0kRrI1OWsjrPMWXpwrwZuXBnb2VyxDBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ddb9676163609fcb316b8ea5f1ee9c22c00d4c1ac5588d4d1244ec38921f8ace","last_reissued_at":"2026-05-18T03:49:22.704308Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:49:22.704308Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0707.3404","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":"2026-05-18T03:49:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X3SVLUkUo0PbQkgdJf2gz2q2BoxELnNdT7F0BTjfZsNGRfMwUTk7PhukHgXaZck89qJXpbzgNT8JJEuMjixBCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T12:01:51.142016Z"},"content_sha256":"108b64a1171a92d6ed195252e486dd800683c77835d4db8a7430a3df1c2e9b05","schema_version":"1.0","event_id":"sha256:108b64a1171a92d6ed195252e486dd800683c77835d4db8a7430a3df1c2e9b05"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:3W4WOYLDMCP4WMLLR2S7D3U4EL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Kouchnirenko type formulas for local invariants of plane analytic curves","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Janusz Gwozdziewicz","submitted_at":"2007-07-23T16:01:42Z","abstract_excerpt":"Let f(x,y)=0 be an equation of plane analytic curve defined in the neighborhood of the origin and let $\\pi:M\\to(\\Cn^2,0)$ be a local toric modification. We give a formula which connects a number of double points \\delta_0(f)$ with a sum $\\sum_p \\delta_p(\\tilde f)$ which runs over all intersection points of the proper preimage of f=0 with the exceptional divisor."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.3404","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":"2026-05-18T03:49:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PThLvxq+eydS7EqTIOPp0okqzgV4zXthMLigJm3tSTH9vcVlYIagx2HVgHWvt7dOK0ZDPdg3ucsjGVra+vZZDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T12:01:51.142377Z"},"content_sha256":"8893eeb565a17b35047407c28364cccede06ea24a16425bf7b54057f9b023656","schema_version":"1.0","event_id":"sha256:8893eeb565a17b35047407c28364cccede06ea24a16425bf7b54057f9b023656"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3W4WOYLDMCP4WMLLR2S7D3U4EL/bundle.json","state_url":"https://pith.science/pith/3W4WOYLDMCP4WMLLR2S7D3U4EL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3W4WOYLDMCP4WMLLR2S7D3U4EL/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":"2026-06-22T12:01:51Z","links":{"resolver":"https://pith.science/pith/3W4WOYLDMCP4WMLLR2S7D3U4EL","bundle":"https://pith.science/pith/3W4WOYLDMCP4WMLLR2S7D3U4EL/bundle.json","state":"https://pith.science/pith/3W4WOYLDMCP4WMLLR2S7D3U4EL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3W4WOYLDMCP4WMLLR2S7D3U4EL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:3W4WOYLDMCP4WMLLR2S7D3U4EL","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":"f19d3d66c8bd9d2b358ef2c37432db846829e8df650fd07eec87c43f4e9013fe","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2007-07-23T16:01:42Z","title_canon_sha256":"6eecb2f9902133aeb0e8deadabd2528fcece6c2a4481888708fabdcdf5d442ef"},"schema_version":"1.0","source":{"id":"0707.3404","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0707.3404","created_at":"2026-05-18T03:49:22Z"},{"alias_kind":"arxiv_version","alias_value":"0707.3404v1","created_at":"2026-05-18T03:49:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0707.3404","created_at":"2026-05-18T03:49:22Z"},{"alias_kind":"pith_short_12","alias_value":"3W4WOYLDMCP4","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"3W4WOYLDMCP4WMLL","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"3W4WOYLD","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:8893eeb565a17b35047407c28364cccede06ea24a16425bf7b54057f9b023656","target":"graph","created_at":"2026-05-18T03:49:22Z","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 f(x,y)=0 be an equation of plane analytic curve defined in the neighborhood of the origin and let $\\pi:M\\to(\\Cn^2,0)$ be a local toric modification. We give a formula which connects a number of double points \\delta_0(f)$ with a sum $\\sum_p \\delta_p(\\tilde f)$ which runs over all intersection points of the proper preimage of f=0 with the exceptional divisor.","authors_text":"Janusz Gwozdziewicz","cross_cats":[],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2007-07-23T16:01:42Z","title":"Kouchnirenko type formulas for local invariants of plane analytic curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.3404","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":"sha256:108b64a1171a92d6ed195252e486dd800683c77835d4db8a7430a3df1c2e9b05","target":"record","created_at":"2026-05-18T03:49:22Z","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":"f19d3d66c8bd9d2b358ef2c37432db846829e8df650fd07eec87c43f4e9013fe","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2007-07-23T16:01:42Z","title_canon_sha256":"6eecb2f9902133aeb0e8deadabd2528fcece6c2a4481888708fabdcdf5d442ef"},"schema_version":"1.0","source":{"id":"0707.3404","kind":"arxiv","version":1}},"canonical_sha256":"ddb9676163609fcb316b8ea5f1ee9c22c00d4c1ac5588d4d1244ec38921f8ace","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ddb9676163609fcb316b8ea5f1ee9c22c00d4c1ac5588d4d1244ec38921f8ace","first_computed_at":"2026-05-18T03:49:22.704308Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:49:22.704308Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WFsseiEW8zfZNtY6NObfFw89orMUxupq7zM7ZeyvWDS/kI5iFCfJnL0kRrI1OWsjrPMWXpwrwZuXBnb2VyxDBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:49:22.705008Z","signed_message":"canonical_sha256_bytes"},"source_id":"0707.3404","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:108b64a1171a92d6ed195252e486dd800683c77835d4db8a7430a3df1c2e9b05","sha256:8893eeb565a17b35047407c28364cccede06ea24a16425bf7b54057f9b023656"],"state_sha256":"709eb1f026325d06f09281872a9e3e6f79be84c98b0d9fde18e18024ad4b68c6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LCsmHz3m5UJeopZL/LzbgeNe8e98bQgpM8lppdo3aQA64D4d5caQ2uL86D8N5YhqStWgfCHy9RPmKrAZR1bgCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T12:01:51.144343Z","bundle_sha256":"ec6ee7755c70ae7e98c955323361c439b3ba96baa35992b0b595bbf6a1f87dcf"}}