{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:WRHYFDFGKNGTJWJBABPIGY47A4","short_pith_number":"pith:WRHYFDFG","canonical_record":{"source":{"id":"0801.4404","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-01-29T00:08:24Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"0842db82b6c897e1e880d07c3b5bd50721f78ff0136076e09cf081c4a4b5ca5f","abstract_canon_sha256":"164d6f9b15e26edb14fe0cbf79a9ffbceb175cf460eeaba20ba80571db164600"},"schema_version":"1.0"},"canonical_sha256":"b44f828ca6534d34d921005e83639f0726d937bd900702b68ed55939e944ea4f","source":{"kind":"arxiv","id":"0801.4404","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0801.4404","created_at":"2026-05-18T00:18:32Z"},{"alias_kind":"arxiv_version","alias_value":"0801.4404v2","created_at":"2026-05-18T00:18:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0801.4404","created_at":"2026-05-18T00:18:32Z"},{"alias_kind":"pith_short_12","alias_value":"WRHYFDFGKNGT","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"WRHYFDFGKNGTJWJB","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"WRHYFDFG","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:WRHYFDFGKNGTJWJBABPIGY47A4","target":"record","payload":{"canonical_record":{"source":{"id":"0801.4404","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-01-29T00:08:24Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"0842db82b6c897e1e880d07c3b5bd50721f78ff0136076e09cf081c4a4b5ca5f","abstract_canon_sha256":"164d6f9b15e26edb14fe0cbf79a9ffbceb175cf460eeaba20ba80571db164600"},"schema_version":"1.0"},"canonical_sha256":"b44f828ca6534d34d921005e83639f0726d937bd900702b68ed55939e944ea4f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:32.418922Z","signature_b64":"AowWyT6XydxFfko/BJFJcAIdIzF03IcENnzzgcR+umUI3o1/LAkDP+rBa9isbZiPm/jQVaY8QqJBIMYTK7SCBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b44f828ca6534d34d921005e83639f0726d937bd900702b68ed55939e944ea4f","last_reissued_at":"2026-05-18T00:18:32.418543Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:32.418543Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0801.4404","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":"2026-05-18T00:18:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UgiCNo7idI77O7g7U5CbayJXKOdRHcyMf+tPFpLU3NmcB7t1DcdX/yA0WSyUmyr0aXHmcH5jyVJGLlpltm5cAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T07:03:45.509722Z"},"content_sha256":"efc811440511ca88e65bc9a6408cb53457e8ce85f79be4adcd2b4911104e147c","schema_version":"1.0","event_id":"sha256:efc811440511ca88e65bc9a6408cb53457e8ce85f79be4adcd2b4911104e147c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:WRHYFDFGKNGTJWJBABPIGY47A4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some relational structures with polynomial growth and their associated algebras II: Finite generation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.CO","authors_text":"Maurice Pouzet, Nicolas M. Thi\\'ery","submitted_at":"2008-01-29T00:08:24Z","abstract_excerpt":"The profile of a relational structure $R$ is the function $\\varphi_R$ which counts for every integer $n$ the number, possibly infinite, $\\varphi_R(n)$ of substructures of $R$ induced on the $n$-element subsets, isomorphic substructures being identified. If $\\varphi_R$ takes only finite values, this is the Hilbert function of a graded algebra associated with $R$, the age algebra $A(R)$, introduced by P.~J.~Cameron.\n  In a previous paper, we studied the relationship between the properties of a relational structure and those of their algebra, particularly when the relational structure $R$ admits "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.4404","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":"2026-05-18T00:18:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KdrtjLz0cuyl2LcS+cNhy4cYkxi97clmUBF0Az0HN7ZrDBRRY8ZEPbALur3Of7sAkqV9Yf0xTFXLpqzvyYpGDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T07:03:45.510122Z"},"content_sha256":"27932bb796423f376a2779b748a0f037b415c227b2de7abc0ea5a6b257bfa233","schema_version":"1.0","event_id":"sha256:27932bb796423f376a2779b748a0f037b415c227b2de7abc0ea5a6b257bfa233"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WRHYFDFGKNGTJWJBABPIGY47A4/bundle.json","state_url":"https://pith.science/pith/WRHYFDFGKNGTJWJBABPIGY47A4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WRHYFDFGKNGTJWJBABPIGY47A4/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":"2026-05-27T07:03:45Z","links":{"resolver":"https://pith.science/pith/WRHYFDFGKNGTJWJBABPIGY47A4","bundle":"https://pith.science/pith/WRHYFDFGKNGTJWJBABPIGY47A4/bundle.json","state":"https://pith.science/pith/WRHYFDFGKNGTJWJBABPIGY47A4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WRHYFDFGKNGTJWJBABPIGY47A4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:WRHYFDFGKNGTJWJBABPIGY47A4","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":"164d6f9b15e26edb14fe0cbf79a9ffbceb175cf460eeaba20ba80571db164600","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-01-29T00:08:24Z","title_canon_sha256":"0842db82b6c897e1e880d07c3b5bd50721f78ff0136076e09cf081c4a4b5ca5f"},"schema_version":"1.0","source":{"id":"0801.4404","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0801.4404","created_at":"2026-05-18T00:18:32Z"},{"alias_kind":"arxiv_version","alias_value":"0801.4404v2","created_at":"2026-05-18T00:18:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0801.4404","created_at":"2026-05-18T00:18:32Z"},{"alias_kind":"pith_short_12","alias_value":"WRHYFDFGKNGT","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"WRHYFDFGKNGTJWJB","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"WRHYFDFG","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:27932bb796423f376a2779b748a0f037b415c227b2de7abc0ea5a6b257bfa233","target":"graph","created_at":"2026-05-18T00:18:32Z","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 profile of a relational structure $R$ is the function $\\varphi_R$ which counts for every integer $n$ the number, possibly infinite, $\\varphi_R(n)$ of substructures of $R$ induced on the $n$-element subsets, isomorphic substructures being identified. If $\\varphi_R$ takes only finite values, this is the Hilbert function of a graded algebra associated with $R$, the age algebra $A(R)$, introduced by P.~J.~Cameron.\n  In a previous paper, we studied the relationship between the properties of a relational structure and those of their algebra, particularly when the relational structure $R$ admits ","authors_text":"Maurice Pouzet, Nicolas M. Thi\\'ery","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-01-29T00:08:24Z","title":"Some relational structures with polynomial growth and their associated algebras II: Finite generation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.4404","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:efc811440511ca88e65bc9a6408cb53457e8ce85f79be4adcd2b4911104e147c","target":"record","created_at":"2026-05-18T00:18:32Z","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":"164d6f9b15e26edb14fe0cbf79a9ffbceb175cf460eeaba20ba80571db164600","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-01-29T00:08:24Z","title_canon_sha256":"0842db82b6c897e1e880d07c3b5bd50721f78ff0136076e09cf081c4a4b5ca5f"},"schema_version":"1.0","source":{"id":"0801.4404","kind":"arxiv","version":2}},"canonical_sha256":"b44f828ca6534d34d921005e83639f0726d937bd900702b68ed55939e944ea4f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b44f828ca6534d34d921005e83639f0726d937bd900702b68ed55939e944ea4f","first_computed_at":"2026-05-18T00:18:32.418543Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:32.418543Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AowWyT6XydxFfko/BJFJcAIdIzF03IcENnzzgcR+umUI3o1/LAkDP+rBa9isbZiPm/jQVaY8QqJBIMYTK7SCBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:32.418922Z","signed_message":"canonical_sha256_bytes"},"source_id":"0801.4404","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:efc811440511ca88e65bc9a6408cb53457e8ce85f79be4adcd2b4911104e147c","sha256:27932bb796423f376a2779b748a0f037b415c227b2de7abc0ea5a6b257bfa233"],"state_sha256":"75453f16e1c2a688e2ba9082b40628a3b5e40d9a1ac9eb84eb336bd2ecbbabb4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GkUZbIWLpN86QUvAPpr1chWMJLTpHHf7aVpGWWVvJgnMAiJ5FuhT5hKu3UQHW4W2tpzmoCcIaXG+lDe1swpXAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T07:03:45.513249Z","bundle_sha256":"6db1b3bd0bb359e1c457a83426459eb5fc5518fac7d21c715fe4f0b8ba688782"}}