{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:SG5RCM3N5NVRIDYV4SDXW75TGX","short_pith_number":"pith:SG5RCM3N","canonical_record":{"source":{"id":"1512.07507","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-12-23T15:08:58Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"a400d57d823500b27e4c5ecc85fd82d42fd86427acb4bd999814e3c54dec45c2","abstract_canon_sha256":"5fb30866cdcd78fa0d8d1b6ec906755e330b88795e6deb3f05d44ecd59bc392a"},"schema_version":"1.0"},"canonical_sha256":"91bb11336deb6b140f15e4877b7fb335e96c4aa6db79750d36b2e199dca1e77d","source":{"kind":"arxiv","id":"1512.07507","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.07507","created_at":"2026-05-18T00:14:47Z"},{"alias_kind":"arxiv_version","alias_value":"1512.07507v4","created_at":"2026-05-18T00:14:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.07507","created_at":"2026-05-18T00:14:47Z"},{"alias_kind":"pith_short_12","alias_value":"SG5RCM3N5NVR","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SG5RCM3N5NVRIDYV","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SG5RCM3N","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:SG5RCM3N5NVRIDYV4SDXW75TGX","target":"record","payload":{"canonical_record":{"source":{"id":"1512.07507","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-12-23T15:08:58Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"a400d57d823500b27e4c5ecc85fd82d42fd86427acb4bd999814e3c54dec45c2","abstract_canon_sha256":"5fb30866cdcd78fa0d8d1b6ec906755e330b88795e6deb3f05d44ecd59bc392a"},"schema_version":"1.0"},"canonical_sha256":"91bb11336deb6b140f15e4877b7fb335e96c4aa6db79750d36b2e199dca1e77d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:47.935174Z","signature_b64":"yOciQgzeFOQpgGiv1SAxTSHc0CKfC6DSFxhhmpCroZ/O8oOCf/eHM/hOmDj8SoWVpuqTwUXQiO6tIgh5V6GhDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"91bb11336deb6b140f15e4877b7fb335e96c4aa6db79750d36b2e199dca1e77d","last_reissued_at":"2026-05-18T00:14:47.934770Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:47.934770Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.07507","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:14:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"opzGbWeawOIKobLhc43XjheKiBw1gA7yrm6asYM9qanP21dDPNYY1ehJ9Lt/8yRhxA/PDCsuxrKryqGg44EdAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T22:07:55.516359Z"},"content_sha256":"68609c46e28bf62353e1e9a2e2612283c325823f41eb1bad391276081ca6f050","schema_version":"1.0","event_id":"sha256:68609c46e28bf62353e1e9a2e2612283c325823f41eb1bad391276081ca6f050"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:SG5RCM3N5NVRIDYV4SDXW75TGX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A polyhedral characterization of quasi-ordinary singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Bernd Schober, Hussein Mourtada","submitted_at":"2015-12-23T15:08:58Z","abstract_excerpt":"Given an irreducible hypersurface singularity of dimension $d$ (defined by a polynomial $f\\in K[[ {\\bf x} ]][z]$) and the projection to the affine space defined by $K[[ {\\bf x} ]]$, we construct an invariant which detects whether the singularity is quasi-ordinary with respect to the projection. The construction uses a weighted version of Hironaka's characteristic polyhedron and successive embeddings of the singularity in affine spaces of higher dimensions. When $ f $ is quasi-ordinary, our invariant determines the semigroup of the singularity and hence it encodes the embedded topology of the s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07507","kind":"arxiv","version":4},"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":"2026-05-18T00:14:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Coj1jIGc+GW3njOYeVsT0TV0B3yrcRGUpaiJKoGjHq5FqWNhIaXlSWWs/koK5aAY2YdRfmEC8Y7F0xn9N0HhDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T22:07:55.516717Z"},"content_sha256":"588db8277e18434aaa4260b05f60790348bd7249b4ddc74618ec90e269e5c893","schema_version":"1.0","event_id":"sha256:588db8277e18434aaa4260b05f60790348bd7249b4ddc74618ec90e269e5c893"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SG5RCM3N5NVRIDYV4SDXW75TGX/bundle.json","state_url":"https://pith.science/pith/SG5RCM3N5NVRIDYV4SDXW75TGX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SG5RCM3N5NVRIDYV4SDXW75TGX/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":"2026-06-21T22:07:55Z","links":{"resolver":"https://pith.science/pith/SG5RCM3N5NVRIDYV4SDXW75TGX","bundle":"https://pith.science/pith/SG5RCM3N5NVRIDYV4SDXW75TGX/bundle.json","state":"https://pith.science/pith/SG5RCM3N5NVRIDYV4SDXW75TGX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SG5RCM3N5NVRIDYV4SDXW75TGX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SG5RCM3N5NVRIDYV4SDXW75TGX","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":"5fb30866cdcd78fa0d8d1b6ec906755e330b88795e6deb3f05d44ecd59bc392a","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-12-23T15:08:58Z","title_canon_sha256":"a400d57d823500b27e4c5ecc85fd82d42fd86427acb4bd999814e3c54dec45c2"},"schema_version":"1.0","source":{"id":"1512.07507","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.07507","created_at":"2026-05-18T00:14:47Z"},{"alias_kind":"arxiv_version","alias_value":"1512.07507v4","created_at":"2026-05-18T00:14:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.07507","created_at":"2026-05-18T00:14:47Z"},{"alias_kind":"pith_short_12","alias_value":"SG5RCM3N5NVR","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SG5RCM3N5NVRIDYV","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SG5RCM3N","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:588db8277e18434aaa4260b05f60790348bd7249b4ddc74618ec90e269e5c893","target":"graph","created_at":"2026-05-18T00:14:47Z","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":"Given an irreducible hypersurface singularity of dimension $d$ (defined by a polynomial $f\\in K[[ {\\bf x} ]][z]$) and the projection to the affine space defined by $K[[ {\\bf x} ]]$, we construct an invariant which detects whether the singularity is quasi-ordinary with respect to the projection. The construction uses a weighted version of Hironaka's characteristic polyhedron and successive embeddings of the singularity in affine spaces of higher dimensions. When $ f $ is quasi-ordinary, our invariant determines the semigroup of the singularity and hence it encodes the embedded topology of the s","authors_text":"Bernd Schober, Hussein Mourtada","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-12-23T15:08:58Z","title":"A polyhedral characterization of quasi-ordinary singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07507","kind":"arxiv","version":4},"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":"sha256:68609c46e28bf62353e1e9a2e2612283c325823f41eb1bad391276081ca6f050","target":"record","created_at":"2026-05-18T00:14:47Z","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":"5fb30866cdcd78fa0d8d1b6ec906755e330b88795e6deb3f05d44ecd59bc392a","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-12-23T15:08:58Z","title_canon_sha256":"a400d57d823500b27e4c5ecc85fd82d42fd86427acb4bd999814e3c54dec45c2"},"schema_version":"1.0","source":{"id":"1512.07507","kind":"arxiv","version":4}},"canonical_sha256":"91bb11336deb6b140f15e4877b7fb335e96c4aa6db79750d36b2e199dca1e77d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"91bb11336deb6b140f15e4877b7fb335e96c4aa6db79750d36b2e199dca1e77d","first_computed_at":"2026-05-18T00:14:47.934770Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:47.934770Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yOciQgzeFOQpgGiv1SAxTSHc0CKfC6DSFxhhmpCroZ/O8oOCf/eHM/hOmDj8SoWVpuqTwUXQiO6tIgh5V6GhDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:47.935174Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.07507","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:68609c46e28bf62353e1e9a2e2612283c325823f41eb1bad391276081ca6f050","sha256:588db8277e18434aaa4260b05f60790348bd7249b4ddc74618ec90e269e5c893"],"state_sha256":"0d4a497a687759247b2df7dea066743f4e0f1b5a6ea382deef25ff8c79b7a369"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pui1JTguUuK2/tfB/iZypwbwojdDmPCQ1PjrmI05g9toVWlqy92CYhdl6oMu63U2olBYW6lAa0VDdunfhSpdCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T22:07:55.518694Z","bundle_sha256":"2f05cf1d6e3d4de6aa7df8c07381525fd5a2d2b31b13110d11da0f42fed49336"}}