{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:XGFSTXCABSA4YADWKW57VB7WNN","short_pith_number":"pith:XGFSTXCA","canonical_record":{"source":{"id":"1106.2355","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-06-12T22:57:07Z","cross_cats_sorted":[],"title_canon_sha256":"87abb0443cfe46ba8ec223a6c1a506e3c6c1797e19f7252271f57707824661f1","abstract_canon_sha256":"7249035023ff6b576e09b727178ce6bbc9712e1137395fe39469820e6bfe827a"},"schema_version":"1.0"},"canonical_sha256":"b98b29dc400c81cc007655bbfa87f66b5d6bee4a001a0a81f531d7ae38bb5ccb","source":{"kind":"arxiv","id":"1106.2355","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.2355","created_at":"2026-05-18T04:20:05Z"},{"alias_kind":"arxiv_version","alias_value":"1106.2355v1","created_at":"2026-05-18T04:20:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.2355","created_at":"2026-05-18T04:20:05Z"},{"alias_kind":"pith_short_12","alias_value":"XGFSTXCABSA4","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"XGFSTXCABSA4YADW","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"XGFSTXCA","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:XGFSTXCABSA4YADWKW57VB7WNN","target":"record","payload":{"canonical_record":{"source":{"id":"1106.2355","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-06-12T22:57:07Z","cross_cats_sorted":[],"title_canon_sha256":"87abb0443cfe46ba8ec223a6c1a506e3c6c1797e19f7252271f57707824661f1","abstract_canon_sha256":"7249035023ff6b576e09b727178ce6bbc9712e1137395fe39469820e6bfe827a"},"schema_version":"1.0"},"canonical_sha256":"b98b29dc400c81cc007655bbfa87f66b5d6bee4a001a0a81f531d7ae38bb5ccb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:05.930219Z","signature_b64":"XxrW7aa05bIFVfmM8Fu4wkmOn8V+vc8kDw3zBTcMKnAcjgzRjW7DV7rGQmM+/JNSHfV7rtu2gXZcsChJgLMYAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b98b29dc400c81cc007655bbfa87f66b5d6bee4a001a0a81f531d7ae38bb5ccb","last_reissued_at":"2026-05-18T04:20:05.929739Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:05.929739Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.2355","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":"2026-05-18T04:20:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1NLjmDw4SP2bsTfsW/2om2BAmjVMmQOZ4Ak/LyKRDaAMWsDt/n7J3xzHgKMH4LzjNuw0n7kp9LeEQpY6jRKgCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T04:15:15.773360Z"},"content_sha256":"42fb4879723ce914a4312a384783af11ba2cc5f567c8b421ad425a325b366f9b","schema_version":"1.0","event_id":"sha256:42fb4879723ce914a4312a384783af11ba2cc5f567c8b421ad425a325b366f9b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:XGFSTXCABSA4YADWKW57VB7WNN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stabilization of Betti Tables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Gwyneth Whieldon","submitted_at":"2011-06-12T22:57:07Z","abstract_excerpt":"Let $I\\subseteq R=\\kk[x_1,...,x_n]$ be a homogeneous equigenerated ideal of degree $r$. We show here that the shapes of the Betti tables of the ideals $I^d$ stabilize, in the sense that there exists some $D$ such that for all $d\\geq D$, $\\betti{i}{j+rd}(I^d)\\neq 0\\Leftrightarrow \\betti{i}{j+rD}(I^D)\\neq 0$. We also produce upper bounds for the stabilization index $\\Stab(I)$. This strengthens the result of Cutkosky, Herzog, and Trung that the Castelnuovo-Mumford regularity $\\reg(I^d)$ is eventually a linear function in $d$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.2355","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":"2026-05-18T04:20:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0NXQSei6mhFZ1rFN53pwm0Oq+aTPANJ6nTHnvrKJWupgXeiYDyODuKh2y1SQUaaWvgv54lXOuCQibaRSxLHOCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T04:15:15.773712Z"},"content_sha256":"484842160190a85e2876b4f6dcbc56dac8e34ea40dc78fe2dff562442b0c6784","schema_version":"1.0","event_id":"sha256:484842160190a85e2876b4f6dcbc56dac8e34ea40dc78fe2dff562442b0c6784"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XGFSTXCABSA4YADWKW57VB7WNN/bundle.json","state_url":"https://pith.science/pith/XGFSTXCABSA4YADWKW57VB7WNN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XGFSTXCABSA4YADWKW57VB7WNN/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":"2026-06-22T04:15:15Z","links":{"resolver":"https://pith.science/pith/XGFSTXCABSA4YADWKW57VB7WNN","bundle":"https://pith.science/pith/XGFSTXCABSA4YADWKW57VB7WNN/bundle.json","state":"https://pith.science/pith/XGFSTXCABSA4YADWKW57VB7WNN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XGFSTXCABSA4YADWKW57VB7WNN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:XGFSTXCABSA4YADWKW57VB7WNN","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":"7249035023ff6b576e09b727178ce6bbc9712e1137395fe39469820e6bfe827a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-06-12T22:57:07Z","title_canon_sha256":"87abb0443cfe46ba8ec223a6c1a506e3c6c1797e19f7252271f57707824661f1"},"schema_version":"1.0","source":{"id":"1106.2355","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.2355","created_at":"2026-05-18T04:20:05Z"},{"alias_kind":"arxiv_version","alias_value":"1106.2355v1","created_at":"2026-05-18T04:20:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.2355","created_at":"2026-05-18T04:20:05Z"},{"alias_kind":"pith_short_12","alias_value":"XGFSTXCABSA4","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"XGFSTXCABSA4YADW","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"XGFSTXCA","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:484842160190a85e2876b4f6dcbc56dac8e34ea40dc78fe2dff562442b0c6784","target":"graph","created_at":"2026-05-18T04:20:05Z","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 $I\\subseteq R=\\kk[x_1,...,x_n]$ be a homogeneous equigenerated ideal of degree $r$. We show here that the shapes of the Betti tables of the ideals $I^d$ stabilize, in the sense that there exists some $D$ such that for all $d\\geq D$, $\\betti{i}{j+rd}(I^d)\\neq 0\\Leftrightarrow \\betti{i}{j+rD}(I^D)\\neq 0$. We also produce upper bounds for the stabilization index $\\Stab(I)$. This strengthens the result of Cutkosky, Herzog, and Trung that the Castelnuovo-Mumford regularity $\\reg(I^d)$ is eventually a linear function in $d$.","authors_text":"Gwyneth Whieldon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-06-12T22:57:07Z","title":"Stabilization of Betti Tables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.2355","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":"sha256:42fb4879723ce914a4312a384783af11ba2cc5f567c8b421ad425a325b366f9b","target":"record","created_at":"2026-05-18T04:20:05Z","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":"7249035023ff6b576e09b727178ce6bbc9712e1137395fe39469820e6bfe827a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-06-12T22:57:07Z","title_canon_sha256":"87abb0443cfe46ba8ec223a6c1a506e3c6c1797e19f7252271f57707824661f1"},"schema_version":"1.0","source":{"id":"1106.2355","kind":"arxiv","version":1}},"canonical_sha256":"b98b29dc400c81cc007655bbfa87f66b5d6bee4a001a0a81f531d7ae38bb5ccb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b98b29dc400c81cc007655bbfa87f66b5d6bee4a001a0a81f531d7ae38bb5ccb","first_computed_at":"2026-05-18T04:20:05.929739Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:05.929739Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XxrW7aa05bIFVfmM8Fu4wkmOn8V+vc8kDw3zBTcMKnAcjgzRjW7DV7rGQmM+/JNSHfV7rtu2gXZcsChJgLMYAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:05.930219Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.2355","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:42fb4879723ce914a4312a384783af11ba2cc5f567c8b421ad425a325b366f9b","sha256:484842160190a85e2876b4f6dcbc56dac8e34ea40dc78fe2dff562442b0c6784"],"state_sha256":"8e4064ddc671effa6888b373c7f96712d326ccbb466e9bc582a1056099d82a95"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zpfz0W7O2h4LPHTmU6gp5uz+/vqmTRJF1K7FQIjOHC4XRo6iSUso9eSwEM1PeP0imJb/qXebpDdbXRURlDB/CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T04:15:15.776163Z","bundle_sha256":"30abf1b77adaf05b0d728e835546087bfe8d0c0527bfce06a77ed48283c79548"}}