{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:D7OLKFCVSQIAYARLGGJGUIXWN3","short_pith_number":"pith:D7OLKFCV","canonical_record":{"source":{"id":"1812.07539","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-12-18T18:16:16Z","cross_cats_sorted":[],"title_canon_sha256":"6f7dc7e6369668604345a9a79db4ee8747c365cf7576904c5c707b7ab727e112","abstract_canon_sha256":"3ccaf7f44a5e9adb0fa695e9caa344f71a932818213c7df3d275e3f841335eec"},"schema_version":"1.0"},"canonical_sha256":"1fdcb5145594100c022b31926a22f66ee687ee75b23e3f5a9f769543e43fda45","source":{"kind":"arxiv","id":"1812.07539","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.07539","created_at":"2026-05-17T23:58:00Z"},{"alias_kind":"arxiv_version","alias_value":"1812.07539v1","created_at":"2026-05-17T23:58:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.07539","created_at":"2026-05-17T23:58:00Z"},{"alias_kind":"pith_short_12","alias_value":"D7OLKFCVSQIA","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"D7OLKFCVSQIAYARL","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"D7OLKFCV","created_at":"2026-05-18T12:32:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:D7OLKFCVSQIAYARLGGJGUIXWN3","target":"record","payload":{"canonical_record":{"source":{"id":"1812.07539","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-12-18T18:16:16Z","cross_cats_sorted":[],"title_canon_sha256":"6f7dc7e6369668604345a9a79db4ee8747c365cf7576904c5c707b7ab727e112","abstract_canon_sha256":"3ccaf7f44a5e9adb0fa695e9caa344f71a932818213c7df3d275e3f841335eec"},"schema_version":"1.0"},"canonical_sha256":"1fdcb5145594100c022b31926a22f66ee687ee75b23e3f5a9f769543e43fda45","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:00.218156Z","signature_b64":"EubsQZbkAFe++2gTuUqdEt0F12fl2fbeeHu9EvAH4FOqv4YlksaMHc6wW1gc9AOrh24NHiTU+UhLnW/KGdm0AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1fdcb5145594100c022b31926a22f66ee687ee75b23e3f5a9f769543e43fda45","last_reissued_at":"2026-05-17T23:58:00.217485Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:00.217485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.07539","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":"2026-05-17T23:58:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OM8Rl+Nu9v46X/jQxQYH+yjXgR143TGoTlGHMuDAYTd2YZj/CjL2mMZCBvt7YKDFfTx0GMQfLi6bzki2YaHmCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T11:19:46.053072Z"},"content_sha256":"41d5b213efc662d4b7d729b7e22af5806a78f232308f959fed922d19a2e5ea04","schema_version":"1.0","event_id":"sha256:41d5b213efc662d4b7d729b7e22af5806a78f232308f959fed922d19a2e5ea04"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:D7OLKFCVSQIAYARLGGJGUIXWN3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Eisenbud-Green-Harris Conjecture for Defect Two Quadratic Ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Melvin Hochster, Sema Gunturkun","submitted_at":"2018-12-18T18:16:16Z","abstract_excerpt":"The Eisenbud-Green-Harris (EGH) conjecture states that a homogeneous ideal in a polynomial ring $K[x_1,\\,\\ldots,\\,x_n]$ over a field $K$ that contains a regular sequence $f_1,\\,\\ldots,\\, f_n$ with degrees $a_i$, $i=1,\\,\\ldots,\\,n$ has the same Hilbert function as a lex-plus-powers ideal containing the powers $x_i^{a_i}$, $i=1,\\,\\ldots,\\,n$. In this paper, we discuss a case of the EGH conjecture for homogeneous ideals generated by $n+2$ quadrics containing a regular sequence $f_1,\\, \\ldots, \\, f_n$ and give a complete proof for EGH when $n=5$ and $a_1=\\cdots=a_5=2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.07539","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":"2026-05-17T23:58:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kh1NUzQBurhVqhJCS1DZ+2fXc9oO8SMXrDvdh49o5nZQzbXd/ZrADbVFoUpO5a5E3XVRaVOFLXFraKqpCxiOCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T11:19:46.053444Z"},"content_sha256":"7a0517f8d445e5d077cf222fc030e91ac27d35ce55921487311981b1782d92a6","schema_version":"1.0","event_id":"sha256:7a0517f8d445e5d077cf222fc030e91ac27d35ce55921487311981b1782d92a6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D7OLKFCVSQIAYARLGGJGUIXWN3/bundle.json","state_url":"https://pith.science/pith/D7OLKFCVSQIAYARLGGJGUIXWN3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D7OLKFCVSQIAYARLGGJGUIXWN3/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":"2026-06-01T11:19:46Z","links":{"resolver":"https://pith.science/pith/D7OLKFCVSQIAYARLGGJGUIXWN3","bundle":"https://pith.science/pith/D7OLKFCVSQIAYARLGGJGUIXWN3/bundle.json","state":"https://pith.science/pith/D7OLKFCVSQIAYARLGGJGUIXWN3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D7OLKFCVSQIAYARLGGJGUIXWN3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:D7OLKFCVSQIAYARLGGJGUIXWN3","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":"3ccaf7f44a5e9adb0fa695e9caa344f71a932818213c7df3d275e3f841335eec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-12-18T18:16:16Z","title_canon_sha256":"6f7dc7e6369668604345a9a79db4ee8747c365cf7576904c5c707b7ab727e112"},"schema_version":"1.0","source":{"id":"1812.07539","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.07539","created_at":"2026-05-17T23:58:00Z"},{"alias_kind":"arxiv_version","alias_value":"1812.07539v1","created_at":"2026-05-17T23:58:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.07539","created_at":"2026-05-17T23:58:00Z"},{"alias_kind":"pith_short_12","alias_value":"D7OLKFCVSQIA","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"D7OLKFCVSQIAYARL","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"D7OLKFCV","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:7a0517f8d445e5d077cf222fc030e91ac27d35ce55921487311981b1782d92a6","target":"graph","created_at":"2026-05-17T23:58:00Z","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":"The Eisenbud-Green-Harris (EGH) conjecture states that a homogeneous ideal in a polynomial ring $K[x_1,\\,\\ldots,\\,x_n]$ over a field $K$ that contains a regular sequence $f_1,\\,\\ldots,\\, f_n$ with degrees $a_i$, $i=1,\\,\\ldots,\\,n$ has the same Hilbert function as a lex-plus-powers ideal containing the powers $x_i^{a_i}$, $i=1,\\,\\ldots,\\,n$. In this paper, we discuss a case of the EGH conjecture for homogeneous ideals generated by $n+2$ quadrics containing a regular sequence $f_1,\\, \\ldots, \\, f_n$ and give a complete proof for EGH when $n=5$ and $a_1=\\cdots=a_5=2$.","authors_text":"Melvin Hochster, Sema Gunturkun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-12-18T18:16:16Z","title":"The Eisenbud-Green-Harris Conjecture for Defect Two Quadratic Ideals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.07539","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":"sha256:41d5b213efc662d4b7d729b7e22af5806a78f232308f959fed922d19a2e5ea04","target":"record","created_at":"2026-05-17T23:58:00Z","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":"3ccaf7f44a5e9adb0fa695e9caa344f71a932818213c7df3d275e3f841335eec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-12-18T18:16:16Z","title_canon_sha256":"6f7dc7e6369668604345a9a79db4ee8747c365cf7576904c5c707b7ab727e112"},"schema_version":"1.0","source":{"id":"1812.07539","kind":"arxiv","version":1}},"canonical_sha256":"1fdcb5145594100c022b31926a22f66ee687ee75b23e3f5a9f769543e43fda45","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1fdcb5145594100c022b31926a22f66ee687ee75b23e3f5a9f769543e43fda45","first_computed_at":"2026-05-17T23:58:00.217485Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:00.217485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EubsQZbkAFe++2gTuUqdEt0F12fl2fbeeHu9EvAH4FOqv4YlksaMHc6wW1gc9AOrh24NHiTU+UhLnW/KGdm0AQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:00.218156Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.07539","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:41d5b213efc662d4b7d729b7e22af5806a78f232308f959fed922d19a2e5ea04","sha256:7a0517f8d445e5d077cf222fc030e91ac27d35ce55921487311981b1782d92a6"],"state_sha256":"f7274a08bfc300e297ac8ccbf8714d5d85c8e596daf8d67eeddcb486bffbc614"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GYIm90qI3F885jIuJtxH3DUCNXolWIDxAY2FVJQvJ0R0kpayR5O2D1s4y3JCc6OfpyYI2ZN77Q/FmJRolyWZCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T11:19:46.055369Z","bundle_sha256":"b5e002b0d5e63ec1d7fb9d26e67b09b3aabc44b4f9445e660cf784432cd7e149"}}