{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:4ZXJLRNYMUUP3I33BPSNI6OAZ5","short_pith_number":"pith:4ZXJLRNY","canonical_record":{"source":{"id":"1707.06733","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-07-21T01:27:23Z","cross_cats_sorted":[],"title_canon_sha256":"d51c4f2372e3b972e1358e5e7d0caf7168ce183c61593b2c2e5f9771dab16082","abstract_canon_sha256":"73f75c2f5586144193b59934d228f5027268915cc1463b13935e6384f0804c6a"},"schema_version":"1.0"},"canonical_sha256":"e66e95c5b86528fda37b0be4d479c0cf6777248ccef46459af9a682208bdf322","source":{"kind":"arxiv","id":"1707.06733","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.06733","created_at":"2026-05-18T00:39:51Z"},{"alias_kind":"arxiv_version","alias_value":"1707.06733v1","created_at":"2026-05-18T00:39:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.06733","created_at":"2026-05-18T00:39:51Z"},{"alias_kind":"pith_short_12","alias_value":"4ZXJLRNYMUUP","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4ZXJLRNYMUUP3I33","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4ZXJLRNY","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:4ZXJLRNYMUUP3I33BPSNI6OAZ5","target":"record","payload":{"canonical_record":{"source":{"id":"1707.06733","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-07-21T01:27:23Z","cross_cats_sorted":[],"title_canon_sha256":"d51c4f2372e3b972e1358e5e7d0caf7168ce183c61593b2c2e5f9771dab16082","abstract_canon_sha256":"73f75c2f5586144193b59934d228f5027268915cc1463b13935e6384f0804c6a"},"schema_version":"1.0"},"canonical_sha256":"e66e95c5b86528fda37b0be4d479c0cf6777248ccef46459af9a682208bdf322","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:51.834152Z","signature_b64":"dD0bJat4Vxyl+qvt9Ui2otBDy0zYwcQoHOHGaRC9Ljo13v08sUNV36xoqIroULw5mTWpLRCFnrW4cwW/6YmODA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e66e95c5b86528fda37b0be4d479c0cf6777248ccef46459af9a682208bdf322","last_reissued_at":"2026-05-18T00:39:51.833623Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:51.833623Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.06733","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":"2026-05-18T00:39:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zhaRZAv6B8iy1DAnV9LRxVAkoCyZjKVsR0IRtbHy4FwQ9eH0fY5zWyG4KXTg31CiGt1rpbMUbOhzkoMQ1IHkCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T01:33:30.851533Z"},"content_sha256":"96989df2de05f2d959af5ddd7d0c7e07e68365790cdd68bb9ddc51a1dbe15577","schema_version":"1.0","event_id":"sha256:96989df2de05f2d959af5ddd7d0c7e07e68365790cdd68bb9ddc51a1dbe15577"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:4ZXJLRNYMUUP3I33BPSNI6OAZ5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Abhyankar's Work on Dicritical Divisors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"David Shannon, William Heinzer","submitted_at":"2017-07-21T01:27:23Z","abstract_excerpt":"We discuss the work of Abhyankar on dicritical divisors with a special focus on the algebraic aspects of this work. We also discuss related work on local quadratic transforms, infinitely near points and Rees valuation rings of an ideal."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06733","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":"2026-05-18T00:39:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ppvixbQDYeZ0MviWy9y5vTPurogp4coN1WHcyLY3CPFHm2737jm8Mi18/EIqMWe6SW2P+4VX5TgnppFRYBDfCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T01:33:30.852059Z"},"content_sha256":"56ef2fa5d033ca0498fa0e2f718c0f92e815eb9c2df5478c57e338b01dbe9b76","schema_version":"1.0","event_id":"sha256:56ef2fa5d033ca0498fa0e2f718c0f92e815eb9c2df5478c57e338b01dbe9b76"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4ZXJLRNYMUUP3I33BPSNI6OAZ5/bundle.json","state_url":"https://pith.science/pith/4ZXJLRNYMUUP3I33BPSNI6OAZ5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4ZXJLRNYMUUP3I33BPSNI6OAZ5/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":"2026-05-31T01:33:30Z","links":{"resolver":"https://pith.science/pith/4ZXJLRNYMUUP3I33BPSNI6OAZ5","bundle":"https://pith.science/pith/4ZXJLRNYMUUP3I33BPSNI6OAZ5/bundle.json","state":"https://pith.science/pith/4ZXJLRNYMUUP3I33BPSNI6OAZ5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4ZXJLRNYMUUP3I33BPSNI6OAZ5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4ZXJLRNYMUUP3I33BPSNI6OAZ5","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":"73f75c2f5586144193b59934d228f5027268915cc1463b13935e6384f0804c6a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-07-21T01:27:23Z","title_canon_sha256":"d51c4f2372e3b972e1358e5e7d0caf7168ce183c61593b2c2e5f9771dab16082"},"schema_version":"1.0","source":{"id":"1707.06733","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.06733","created_at":"2026-05-18T00:39:51Z"},{"alias_kind":"arxiv_version","alias_value":"1707.06733v1","created_at":"2026-05-18T00:39:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.06733","created_at":"2026-05-18T00:39:51Z"},{"alias_kind":"pith_short_12","alias_value":"4ZXJLRNYMUUP","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4ZXJLRNYMUUP3I33","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4ZXJLRNY","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:56ef2fa5d033ca0498fa0e2f718c0f92e815eb9c2df5478c57e338b01dbe9b76","target":"graph","created_at":"2026-05-18T00:39:51Z","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 discuss the work of Abhyankar on dicritical divisors with a special focus on the algebraic aspects of this work. We also discuss related work on local quadratic transforms, infinitely near points and Rees valuation rings of an ideal.","authors_text":"David Shannon, William Heinzer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-07-21T01:27:23Z","title":"Abhyankar's Work on Dicritical Divisors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06733","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":"sha256:96989df2de05f2d959af5ddd7d0c7e07e68365790cdd68bb9ddc51a1dbe15577","target":"record","created_at":"2026-05-18T00:39:51Z","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":"73f75c2f5586144193b59934d228f5027268915cc1463b13935e6384f0804c6a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-07-21T01:27:23Z","title_canon_sha256":"d51c4f2372e3b972e1358e5e7d0caf7168ce183c61593b2c2e5f9771dab16082"},"schema_version":"1.0","source":{"id":"1707.06733","kind":"arxiv","version":1}},"canonical_sha256":"e66e95c5b86528fda37b0be4d479c0cf6777248ccef46459af9a682208bdf322","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e66e95c5b86528fda37b0be4d479c0cf6777248ccef46459af9a682208bdf322","first_computed_at":"2026-05-18T00:39:51.833623Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:51.833623Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dD0bJat4Vxyl+qvt9Ui2otBDy0zYwcQoHOHGaRC9Ljo13v08sUNV36xoqIroULw5mTWpLRCFnrW4cwW/6YmODA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:51.834152Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.06733","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96989df2de05f2d959af5ddd7d0c7e07e68365790cdd68bb9ddc51a1dbe15577","sha256:56ef2fa5d033ca0498fa0e2f718c0f92e815eb9c2df5478c57e338b01dbe9b76"],"state_sha256":"2b72592bc4b9b5846d1009405fb01b17a0e44fb9e1484e07606399f6a6d7a679"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aXSRiK46w8R+bFzjdSIj5TJLmPRTlQTq1FyodxECwDzubicgFLhMe9JoVPkAcbIn+HQUh16Ea1shleDBuLc3Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T01:33:30.855521Z","bundle_sha256":"6be765044e6c83043cf5f00a7d7dcee94b4c405153e191d6a358cac20fe87866"}}