{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:VJEPHZUECBF3J5UWZSUGG3RBHG","short_pith_number":"pith:VJEPHZUE","canonical_record":{"source":{"id":"1410.5969","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-10-22T09:49:10Z","cross_cats_sorted":[],"title_canon_sha256":"a31e2aa3d929622064aa5870bfcd8cd6cf0e56779522baf1b3870780ab18f3d8","abstract_canon_sha256":"aafe3b0b8ef64c25ccbfc65b1e9f7f6c9f346433783be20c411168fa8a144bb9"},"schema_version":"1.0"},"canonical_sha256":"aa48f3e684104bb4f696cca8636e2139a984946cbcf00833a198f30db3e94750","source":{"kind":"arxiv","id":"1410.5969","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.5969","created_at":"2026-05-18T02:33:24Z"},{"alias_kind":"arxiv_version","alias_value":"1410.5969v2","created_at":"2026-05-18T02:33:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.5969","created_at":"2026-05-18T02:33:24Z"},{"alias_kind":"pith_short_12","alias_value":"VJEPHZUECBF3","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"VJEPHZUECBF3J5UW","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"VJEPHZUE","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:VJEPHZUECBF3J5UWZSUGG3RBHG","target":"record","payload":{"canonical_record":{"source":{"id":"1410.5969","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-10-22T09:49:10Z","cross_cats_sorted":[],"title_canon_sha256":"a31e2aa3d929622064aa5870bfcd8cd6cf0e56779522baf1b3870780ab18f3d8","abstract_canon_sha256":"aafe3b0b8ef64c25ccbfc65b1e9f7f6c9f346433783be20c411168fa8a144bb9"},"schema_version":"1.0"},"canonical_sha256":"aa48f3e684104bb4f696cca8636e2139a984946cbcf00833a198f30db3e94750","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:33:24.961386Z","signature_b64":"rs+oA8AAye8yT2IK+83InzouDWR5ksbfwwTskZEyzFq9ZJ6fN1N2rZq+Rkr45LOUUzZtfpWWRuq0m8cS+/cfAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa48f3e684104bb4f696cca8636e2139a984946cbcf00833a198f30db3e94750","last_reissued_at":"2026-05-18T02:33:24.960796Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:33:24.960796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.5969","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:33:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0k5S6eLDfNl8jJxbES/UZe7fiwRahrSKWUUqx7z8C+ZF18b/ajcbHk6z/u9Pty/VRTHscc/vXRZV9cYmkz3SCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T16:43:20.837725Z"},"content_sha256":"9c1b0aa895c83fccfbf2e4972a58ff30132c664d7422c962424ab60886557c15","schema_version":"1.0","event_id":"sha256:9c1b0aa895c83fccfbf2e4972a58ff30132c664d7422c962424ab60886557c15"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:VJEPHZUECBF3J5UWZSUGG3RBHG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The converse of a theorem by Bayer and Stillman","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"HyunBin Loh","submitted_at":"2014-10-22T09:49:10Z","abstract_excerpt":"Bayer-Stillman showed that $reg(I) = reg(gin_\\tau(I))$ when $\\tau$ is the graded reverse lexicographic order. We show that the reverse lexicographic order is the unique monomial order $\\tau$ satisfying $reg(I) = reg(gin_\\tau(I))$ for all ideals $I$. We also show that if $gin_{\\tau_1}(I) = gin_{\\tau_2}(I)$ for all $I$, then $\\tau_1 = \\tau_2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5969","kind":"arxiv","version":2},"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":"2026-05-18T02:33:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xCj2KpWh7a27Iye4qB1eG2epAS9cx1mkBrHBcI0JKZ0HCZID2N3Wq9zJ6qMsFyOpva+efx4yk9bIsMIcwWFQDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T16:43:20.838070Z"},"content_sha256":"59b7b5334a14044c921934b5871d2a1e598481d5e912feca88b466bc5102496d","schema_version":"1.0","event_id":"sha256:59b7b5334a14044c921934b5871d2a1e598481d5e912feca88b466bc5102496d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VJEPHZUECBF3J5UWZSUGG3RBHG/bundle.json","state_url":"https://pith.science/pith/VJEPHZUECBF3J5UWZSUGG3RBHG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VJEPHZUECBF3J5UWZSUGG3RBHG/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":"2026-07-01T16:43:20Z","links":{"resolver":"https://pith.science/pith/VJEPHZUECBF3J5UWZSUGG3RBHG","bundle":"https://pith.science/pith/VJEPHZUECBF3J5UWZSUGG3RBHG/bundle.json","state":"https://pith.science/pith/VJEPHZUECBF3J5UWZSUGG3RBHG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VJEPHZUECBF3J5UWZSUGG3RBHG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:VJEPHZUECBF3J5UWZSUGG3RBHG","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":"aafe3b0b8ef64c25ccbfc65b1e9f7f6c9f346433783be20c411168fa8a144bb9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-10-22T09:49:10Z","title_canon_sha256":"a31e2aa3d929622064aa5870bfcd8cd6cf0e56779522baf1b3870780ab18f3d8"},"schema_version":"1.0","source":{"id":"1410.5969","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.5969","created_at":"2026-05-18T02:33:24Z"},{"alias_kind":"arxiv_version","alias_value":"1410.5969v2","created_at":"2026-05-18T02:33:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.5969","created_at":"2026-05-18T02:33:24Z"},{"alias_kind":"pith_short_12","alias_value":"VJEPHZUECBF3","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"VJEPHZUECBF3J5UW","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"VJEPHZUE","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:59b7b5334a14044c921934b5871d2a1e598481d5e912feca88b466bc5102496d","target":"graph","created_at":"2026-05-18T02:33:24Z","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":"Bayer-Stillman showed that $reg(I) = reg(gin_\\tau(I))$ when $\\tau$ is the graded reverse lexicographic order. We show that the reverse lexicographic order is the unique monomial order $\\tau$ satisfying $reg(I) = reg(gin_\\tau(I))$ for all ideals $I$. We also show that if $gin_{\\tau_1}(I) = gin_{\\tau_2}(I)$ for all $I$, then $\\tau_1 = \\tau_2$.","authors_text":"HyunBin Loh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-10-22T09:49:10Z","title":"The converse of a theorem by Bayer and Stillman"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5969","kind":"arxiv","version":2},"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":"sha256:9c1b0aa895c83fccfbf2e4972a58ff30132c664d7422c962424ab60886557c15","target":"record","created_at":"2026-05-18T02:33:24Z","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":"aafe3b0b8ef64c25ccbfc65b1e9f7f6c9f346433783be20c411168fa8a144bb9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-10-22T09:49:10Z","title_canon_sha256":"a31e2aa3d929622064aa5870bfcd8cd6cf0e56779522baf1b3870780ab18f3d8"},"schema_version":"1.0","source":{"id":"1410.5969","kind":"arxiv","version":2}},"canonical_sha256":"aa48f3e684104bb4f696cca8636e2139a984946cbcf00833a198f30db3e94750","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aa48f3e684104bb4f696cca8636e2139a984946cbcf00833a198f30db3e94750","first_computed_at":"2026-05-18T02:33:24.960796Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:33:24.960796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rs+oA8AAye8yT2IK+83InzouDWR5ksbfwwTskZEyzFq9ZJ6fN1N2rZq+Rkr45LOUUzZtfpWWRuq0m8cS+/cfAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:33:24.961386Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.5969","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c1b0aa895c83fccfbf2e4972a58ff30132c664d7422c962424ab60886557c15","sha256:59b7b5334a14044c921934b5871d2a1e598481d5e912feca88b466bc5102496d"],"state_sha256":"089fe19ed3cb1ba704a8fb26f585c211e9fe3ffe37f0d40540f54ac782bfaace"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6/XXs0LxCGJp0dKwWEepS9Q/TPM8anScQ1TmD1eyS93/gDLW5Zt7ifRabXiCvoe1iZp1BZqVaogrBP6UuDXYDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T16:43:20.840180Z","bundle_sha256":"ff16b74a1a39c165495d4d21188bf2ec0454107508c860ba6cc48c6424ea3ab2"}}