{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:KFNJ5BALJYBNKGLXT6XRX7JJS5","short_pith_number":"pith:KFNJ5BAL","canonical_record":{"source":{"id":"1212.4358","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-12-18T14:24:19Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"00854cc42deb09c2b244ff307e0475defed049b6d6c37f5fc6e284cd8851cba8","abstract_canon_sha256":"f767c48a0b711db650a10dee6279196d7407d61d79b76ec654f00031e5c8b17e"},"schema_version":"1.0"},"canonical_sha256":"515a9e840b4e02d519779faf1bfd29976534583ec47ecff24500c138bd436f69","source":{"kind":"arxiv","id":"1212.4358","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.4358","created_at":"2026-05-18T01:22:58Z"},{"alias_kind":"arxiv_version","alias_value":"1212.4358v1","created_at":"2026-05-18T01:22:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.4358","created_at":"2026-05-18T01:22:58Z"},{"alias_kind":"pith_short_12","alias_value":"KFNJ5BALJYBN","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KFNJ5BALJYBNKGLX","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KFNJ5BAL","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:KFNJ5BALJYBNKGLXT6XRX7JJS5","target":"record","payload":{"canonical_record":{"source":{"id":"1212.4358","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-12-18T14:24:19Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"00854cc42deb09c2b244ff307e0475defed049b6d6c37f5fc6e284cd8851cba8","abstract_canon_sha256":"f767c48a0b711db650a10dee6279196d7407d61d79b76ec654f00031e5c8b17e"},"schema_version":"1.0"},"canonical_sha256":"515a9e840b4e02d519779faf1bfd29976534583ec47ecff24500c138bd436f69","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:58.148113Z","signature_b64":"Jwyeey9ubfn49tV+QtzDNfKDUBpm/zcxFG50PMNiXeh7MrizWCzkgEdRLg2OtxliUGYIslxCbOhtM2LR40pYCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"515a9e840b4e02d519779faf1bfd29976534583ec47ecff24500c138bd436f69","last_reissued_at":"2026-05-18T01:22:58.147526Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:58.147526Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.4358","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":"2026-05-18T01:22:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7kFqtjpJj8TWNpLVNgOdrNrZRJ2jZ4uYQX3bjeI/nImdIjJ615nYrG953Iu0IpAlQWQ7pIQTjVs1tds/vxXUBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T11:29:25.673106Z"},"content_sha256":"c3b9d2fb7ddf41cefec4e587d483262c74e7e306303910539414fbbdee27687a","schema_version":"1.0","event_id":"sha256:c3b9d2fb7ddf41cefec4e587d483262c74e7e306303910539414fbbdee27687a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:KFNJ5BALJYBNKGLXT6XRX7JJS5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bounds for the Betti numbers of successive stellar subdivisions of a simplex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Janko Boehm, Stavros Argyrios Papadakis","submitted_at":"2012-12-18T14:24:19Z","abstract_excerpt":"We give a bound for the Betti numbers of the Stanley-Reisner ring of a stellar subdivision of a Gorenstein* simplicial complex by applying unprojection theory. From this we derive a bound for the Betti numbers of iterated stellar subdivisions of the boundary complex of a simplex. The bound depends only on the number of subdivisions, and we construct examples which prove that it is sharp."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4358","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":"2026-05-18T01:22:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jTIC5OSsX0bfkBLzww5SCK1dsl7vNRIfLkQBk9vSW/naOkP/CRwrHn0BDHnJtJfj9j5w4CR4j+azO+0vOZPaCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T11:29:25.673788Z"},"content_sha256":"9106ea05ce74f1b9845b9fb981f23feee940d6d8dfbf39b82ef009b8304bc1e5","schema_version":"1.0","event_id":"sha256:9106ea05ce74f1b9845b9fb981f23feee940d6d8dfbf39b82ef009b8304bc1e5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KFNJ5BALJYBNKGLXT6XRX7JJS5/bundle.json","state_url":"https://pith.science/pith/KFNJ5BALJYBNKGLXT6XRX7JJS5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KFNJ5BALJYBNKGLXT6XRX7JJS5/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":"2026-05-19T11:29:25Z","links":{"resolver":"https://pith.science/pith/KFNJ5BALJYBNKGLXT6XRX7JJS5","bundle":"https://pith.science/pith/KFNJ5BALJYBNKGLXT6XRX7JJS5/bundle.json","state":"https://pith.science/pith/KFNJ5BALJYBNKGLXT6XRX7JJS5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KFNJ5BALJYBNKGLXT6XRX7JJS5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:KFNJ5BALJYBNKGLXT6XRX7JJS5","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":"f767c48a0b711db650a10dee6279196d7407d61d79b76ec654f00031e5c8b17e","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-12-18T14:24:19Z","title_canon_sha256":"00854cc42deb09c2b244ff307e0475defed049b6d6c37f5fc6e284cd8851cba8"},"schema_version":"1.0","source":{"id":"1212.4358","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.4358","created_at":"2026-05-18T01:22:58Z"},{"alias_kind":"arxiv_version","alias_value":"1212.4358v1","created_at":"2026-05-18T01:22:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.4358","created_at":"2026-05-18T01:22:58Z"},{"alias_kind":"pith_short_12","alias_value":"KFNJ5BALJYBN","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KFNJ5BALJYBNKGLX","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KFNJ5BAL","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:9106ea05ce74f1b9845b9fb981f23feee940d6d8dfbf39b82ef009b8304bc1e5","target":"graph","created_at":"2026-05-18T01:22:58Z","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 give a bound for the Betti numbers of the Stanley-Reisner ring of a stellar subdivision of a Gorenstein* simplicial complex by applying unprojection theory. From this we derive a bound for the Betti numbers of iterated stellar subdivisions of the boundary complex of a simplex. The bound depends only on the number of subdivisions, and we construct examples which prove that it is sharp.","authors_text":"Janko Boehm, Stavros Argyrios Papadakis","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-12-18T14:24:19Z","title":"Bounds for the Betti numbers of successive stellar subdivisions of a simplex"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4358","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:c3b9d2fb7ddf41cefec4e587d483262c74e7e306303910539414fbbdee27687a","target":"record","created_at":"2026-05-18T01:22:58Z","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":"f767c48a0b711db650a10dee6279196d7407d61d79b76ec654f00031e5c8b17e","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-12-18T14:24:19Z","title_canon_sha256":"00854cc42deb09c2b244ff307e0475defed049b6d6c37f5fc6e284cd8851cba8"},"schema_version":"1.0","source":{"id":"1212.4358","kind":"arxiv","version":1}},"canonical_sha256":"515a9e840b4e02d519779faf1bfd29976534583ec47ecff24500c138bd436f69","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"515a9e840b4e02d519779faf1bfd29976534583ec47ecff24500c138bd436f69","first_computed_at":"2026-05-18T01:22:58.147526Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:58.147526Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Jwyeey9ubfn49tV+QtzDNfKDUBpm/zcxFG50PMNiXeh7MrizWCzkgEdRLg2OtxliUGYIslxCbOhtM2LR40pYCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:58.148113Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.4358","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3b9d2fb7ddf41cefec4e587d483262c74e7e306303910539414fbbdee27687a","sha256:9106ea05ce74f1b9845b9fb981f23feee940d6d8dfbf39b82ef009b8304bc1e5"],"state_sha256":"8d541b894b2fd6d3c10463857d377686e62f976de2dbea1f207afe4870e87d07"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"18Hy8rbAVgx8XNR0DqAKxMPQsVg6vVfSm73b2f+N0w8gsWIDcazfQXekvY5qCrRpj667r4DffFYCcf6xUvl2CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-19T11:29:25.676688Z","bundle_sha256":"ac874a9ee3e25812d1367c87fa40bd0d9245122eaf708f923cb4175d4f27d9df"}}