{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:7KWDAKP5IBSJ6TUDHERRVKXPKI","short_pith_number":"pith:7KWDAKP5","canonical_record":{"source":{"id":"1705.02230","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-05-05T13:55:16Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"bc32b456ec9b43c30f28dcf75ac753b5fba2edf9321c215f42d1f038b3233dd8","abstract_canon_sha256":"05f2139c259156c1b67d960cd44ea95cfda7f121bdff5ee946413fbf97acdb83"},"schema_version":"1.0"},"canonical_sha256":"faac3029fd40649f4e8339231aaaef521baeac29eb8f4d32bd20fff00c4a156e","source":{"kind":"arxiv","id":"1705.02230","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.02230","created_at":"2026-05-18T00:45:00Z"},{"alias_kind":"arxiv_version","alias_value":"1705.02230v1","created_at":"2026-05-18T00:45:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.02230","created_at":"2026-05-18T00:45:00Z"},{"alias_kind":"pith_short_12","alias_value":"7KWDAKP5IBSJ","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7KWDAKP5IBSJ6TUD","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7KWDAKP5","created_at":"2026-05-18T12:31:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:7KWDAKP5IBSJ6TUDHERRVKXPKI","target":"record","payload":{"canonical_record":{"source":{"id":"1705.02230","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-05-05T13:55:16Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"bc32b456ec9b43c30f28dcf75ac753b5fba2edf9321c215f42d1f038b3233dd8","abstract_canon_sha256":"05f2139c259156c1b67d960cd44ea95cfda7f121bdff5ee946413fbf97acdb83"},"schema_version":"1.0"},"canonical_sha256":"faac3029fd40649f4e8339231aaaef521baeac29eb8f4d32bd20fff00c4a156e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:00.346860Z","signature_b64":"lq+bK1NKUQJ03Y0UN/jREXBxj+wiMKWKg4ERKw/Oyuq7QGJijeg7XuyWJw77Y0dCi2ulfUTT/3bVc0FsLdnHCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"faac3029fd40649f4e8339231aaaef521baeac29eb8f4d32bd20fff00c4a156e","last_reissued_at":"2026-05-18T00:45:00.346420Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:00.346420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.02230","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":"2026-05-18T00:45:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yjTb2P5TklQPDD/Too4oIvlv2ps5ghXXucfKTpCT+eX6pb2uDAJdeXFT3eo2hnAixPNVu/dDfFah0ALfTNTDCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T23:23:11.636808Z"},"content_sha256":"fe50b16a829594098244dff9339cb56f9dffd3152eb3305a6ebbac51ed01fdc1","schema_version":"1.0","event_id":"sha256:fe50b16a829594098244dff9339cb56f9dffd3152eb3305a6ebbac51ed01fdc1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:7KWDAKP5IBSJ6TUDHERRVKXPKI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The {\\L}ojasiewicz Exponent via The Valuative Hamburger-Noether Process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Szymon Brzostowski, Tomasz Rodak","submitted_at":"2017-05-05T13:55:16Z","abstract_excerpt":"Let $k$ be an algebraically closed field of any characteristic. We apply the Hamburger-Noether process of successive quadratic transformations to show the equivalence of two definitions of the {\\L}ojasiewicz exponent $\\mathfrak{L}(\\mathfrak{a})$ of an ideal $\\mathfrak{a}\\subset k[[x,y]]$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02230","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":"2026-05-18T00:45:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+Q3wDMmSM/GBcgON96oLQVMyOEUWgKRG56vPkezFq4wpWv6wxrNXq+iUzFQ9WhiIYAqiRnfy3EYDZd4SFTWODw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T23:23:11.637140Z"},"content_sha256":"720d6a3f79d630764d5031a469976be7d36b3917695b9745cbdf9188bbc65ab4","schema_version":"1.0","event_id":"sha256:720d6a3f79d630764d5031a469976be7d36b3917695b9745cbdf9188bbc65ab4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7KWDAKP5IBSJ6TUDHERRVKXPKI/bundle.json","state_url":"https://pith.science/pith/7KWDAKP5IBSJ6TUDHERRVKXPKI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7KWDAKP5IBSJ6TUDHERRVKXPKI/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":"2026-06-08T23:23:11Z","links":{"resolver":"https://pith.science/pith/7KWDAKP5IBSJ6TUDHERRVKXPKI","bundle":"https://pith.science/pith/7KWDAKP5IBSJ6TUDHERRVKXPKI/bundle.json","state":"https://pith.science/pith/7KWDAKP5IBSJ6TUDHERRVKXPKI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7KWDAKP5IBSJ6TUDHERRVKXPKI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:7KWDAKP5IBSJ6TUDHERRVKXPKI","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":"05f2139c259156c1b67d960cd44ea95cfda7f121bdff5ee946413fbf97acdb83","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-05-05T13:55:16Z","title_canon_sha256":"bc32b456ec9b43c30f28dcf75ac753b5fba2edf9321c215f42d1f038b3233dd8"},"schema_version":"1.0","source":{"id":"1705.02230","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.02230","created_at":"2026-05-18T00:45:00Z"},{"alias_kind":"arxiv_version","alias_value":"1705.02230v1","created_at":"2026-05-18T00:45:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.02230","created_at":"2026-05-18T00:45:00Z"},{"alias_kind":"pith_short_12","alias_value":"7KWDAKP5IBSJ","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7KWDAKP5IBSJ6TUD","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7KWDAKP5","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:720d6a3f79d630764d5031a469976be7d36b3917695b9745cbdf9188bbc65ab4","target":"graph","created_at":"2026-05-18T00:45:00Z","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 $k$ be an algebraically closed field of any characteristic. We apply the Hamburger-Noether process of successive quadratic transformations to show the equivalence of two definitions of the {\\L}ojasiewicz exponent $\\mathfrak{L}(\\mathfrak{a})$ of an ideal $\\mathfrak{a}\\subset k[[x,y]]$.","authors_text":"Szymon Brzostowski, Tomasz Rodak","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-05-05T13:55:16Z","title":"The {\\L}ojasiewicz Exponent via The Valuative Hamburger-Noether Process"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02230","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:fe50b16a829594098244dff9339cb56f9dffd3152eb3305a6ebbac51ed01fdc1","target":"record","created_at":"2026-05-18T00:45:00Z","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":"05f2139c259156c1b67d960cd44ea95cfda7f121bdff5ee946413fbf97acdb83","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-05-05T13:55:16Z","title_canon_sha256":"bc32b456ec9b43c30f28dcf75ac753b5fba2edf9321c215f42d1f038b3233dd8"},"schema_version":"1.0","source":{"id":"1705.02230","kind":"arxiv","version":1}},"canonical_sha256":"faac3029fd40649f4e8339231aaaef521baeac29eb8f4d32bd20fff00c4a156e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"faac3029fd40649f4e8339231aaaef521baeac29eb8f4d32bd20fff00c4a156e","first_computed_at":"2026-05-18T00:45:00.346420Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:00.346420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lq+bK1NKUQJ03Y0UN/jREXBxj+wiMKWKg4ERKw/Oyuq7QGJijeg7XuyWJw77Y0dCi2ulfUTT/3bVc0FsLdnHCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:00.346860Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.02230","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe50b16a829594098244dff9339cb56f9dffd3152eb3305a6ebbac51ed01fdc1","sha256:720d6a3f79d630764d5031a469976be7d36b3917695b9745cbdf9188bbc65ab4"],"state_sha256":"7d52cb68d5eb3e8395699c742714cc097491bc8c98dea4cdbb92edbf4346b302"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I1djSDJL88Bv4pSrKAvD1irrSWg/GBSBGFEOTuo0cxNO+ZNrNnac47ZZGlNxgeWclW34imBag/ktDe3MuvoVCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T23:23:11.638986Z","bundle_sha256":"99d190e8503f55f473c5c88d1f0079e280d0ddb1bed918a203d086ccf83b4554"}}