{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:FHCJMHE57OCXABZACVEOLFZMJQ","short_pith_number":"pith:FHCJMHE5","canonical_record":{"source":{"id":"1306.4109","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-06-18T09:05:53Z","cross_cats_sorted":[],"title_canon_sha256":"4f7e5be553d73ac004828bf3e3d605386861b4e5ed78cbe9c4c30d4b314cef02","abstract_canon_sha256":"7926298ef2dbc42d800e52958df2d1dc927162bd14a44c7a7d23307128808ced"},"schema_version":"1.0"},"canonical_sha256":"29c4961c9dfb857007201548e5972c4c3d45d0ebb236bf1de5f1a36a2cf2e649","source":{"kind":"arxiv","id":"1306.4109","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.4109","created_at":"2026-05-18T03:20:37Z"},{"alias_kind":"arxiv_version","alias_value":"1306.4109v1","created_at":"2026-05-18T03:20:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.4109","created_at":"2026-05-18T03:20:37Z"},{"alias_kind":"pith_short_12","alias_value":"FHCJMHE57OCX","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FHCJMHE57OCXABZA","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FHCJMHE5","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:FHCJMHE57OCXABZACVEOLFZMJQ","target":"record","payload":{"canonical_record":{"source":{"id":"1306.4109","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-06-18T09:05:53Z","cross_cats_sorted":[],"title_canon_sha256":"4f7e5be553d73ac004828bf3e3d605386861b4e5ed78cbe9c4c30d4b314cef02","abstract_canon_sha256":"7926298ef2dbc42d800e52958df2d1dc927162bd14a44c7a7d23307128808ced"},"schema_version":"1.0"},"canonical_sha256":"29c4961c9dfb857007201548e5972c4c3d45d0ebb236bf1de5f1a36a2cf2e649","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:37.132294Z","signature_b64":"WCYPQGqO5noSwqUsUnlPDoozq5Fmf0/utQGXktEOX9P5RpCZ3u1MYb6G8jksXS9mL8++b9Ip3jHvaxaD6iRuCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"29c4961c9dfb857007201548e5972c4c3d45d0ebb236bf1de5f1a36a2cf2e649","last_reissued_at":"2026-05-18T03:20:37.131592Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:37.131592Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.4109","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":"2026-05-18T03:20:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SxA+nyGsAxUxnq1Ngu49PcHASoaPg8mGAqg3IAqeaikmvrgBwABVAvAgaNr4FBBdBMX9Ya5kW0IC/beC9h0BBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T11:12:15.808546Z"},"content_sha256":"2d68e4e5d50cc6b3f78c3d8e88a7cd2770445005db1cc5a893d8697502991e6b","schema_version":"1.0","event_id":"sha256:2d68e4e5d50cc6b3f78c3d8e88a7cd2770445005db1cc5a893d8697502991e6b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:FHCJMHE57OCXABZACVEOLFZMJQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Krull dimension of rings of semialgebraic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"J.M. Gamboa, Jos\\'e F. Fernando","submitted_at":"2013-06-18T09:05:53Z","abstract_excerpt":"Let $R$ be a real closed field and let ${\\mathcal S}(M)$ be the ring of (continuous) semialgebraic functions on a semialgebraic set $M\\subset R^n$ and let ${\\mathcal S}^*(M)$ be its subring of bounded semialgebraic functions. In this work we introduce the concept of \\em semialgebraic depth \\em of a prime ideal $\\gtp$ of ${\\mathcal S}(M)$ in order to provide an elementary proof of the finiteness of the Krull dimension of the rings ${\\mathcal S}(M)$ and ${\\mathcal S}^*(M)$, inspired in the classical way of doing to compute the dimension of a ring of polynomials on a complex algebraic set and wit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.4109","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":"2026-05-18T03:20:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B5sK8qxg+zZO7ays6oPkVOVxnu70wjyVzzSaD17Fh01fIYHcRr0o/P2JcU6hs3vW5ZGmmquYqK0bixwMCRFzCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T11:12:15.808900Z"},"content_sha256":"a6ae2b29c75d7da98cf0c3ecc946b544620dcfe4bc688d6ffbc12029ca19b532","schema_version":"1.0","event_id":"sha256:a6ae2b29c75d7da98cf0c3ecc946b544620dcfe4bc688d6ffbc12029ca19b532"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FHCJMHE57OCXABZACVEOLFZMJQ/bundle.json","state_url":"https://pith.science/pith/FHCJMHE57OCXABZACVEOLFZMJQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FHCJMHE57OCXABZACVEOLFZMJQ/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":"2026-06-22T11:12:15Z","links":{"resolver":"https://pith.science/pith/FHCJMHE57OCXABZACVEOLFZMJQ","bundle":"https://pith.science/pith/FHCJMHE57OCXABZACVEOLFZMJQ/bundle.json","state":"https://pith.science/pith/FHCJMHE57OCXABZACVEOLFZMJQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FHCJMHE57OCXABZACVEOLFZMJQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:FHCJMHE57OCXABZACVEOLFZMJQ","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":"7926298ef2dbc42d800e52958df2d1dc927162bd14a44c7a7d23307128808ced","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-06-18T09:05:53Z","title_canon_sha256":"4f7e5be553d73ac004828bf3e3d605386861b4e5ed78cbe9c4c30d4b314cef02"},"schema_version":"1.0","source":{"id":"1306.4109","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.4109","created_at":"2026-05-18T03:20:37Z"},{"alias_kind":"arxiv_version","alias_value":"1306.4109v1","created_at":"2026-05-18T03:20:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.4109","created_at":"2026-05-18T03:20:37Z"},{"alias_kind":"pith_short_12","alias_value":"FHCJMHE57OCX","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FHCJMHE57OCXABZA","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FHCJMHE5","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:a6ae2b29c75d7da98cf0c3ecc946b544620dcfe4bc688d6ffbc12029ca19b532","target":"graph","created_at":"2026-05-18T03:20:37Z","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 $R$ be a real closed field and let ${\\mathcal S}(M)$ be the ring of (continuous) semialgebraic functions on a semialgebraic set $M\\subset R^n$ and let ${\\mathcal S}^*(M)$ be its subring of bounded semialgebraic functions. In this work we introduce the concept of \\em semialgebraic depth \\em of a prime ideal $\\gtp$ of ${\\mathcal S}(M)$ in order to provide an elementary proof of the finiteness of the Krull dimension of the rings ${\\mathcal S}(M)$ and ${\\mathcal S}^*(M)$, inspired in the classical way of doing to compute the dimension of a ring of polynomials on a complex algebraic set and wit","authors_text":"J.M. Gamboa, Jos\\'e F. Fernando","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-06-18T09:05:53Z","title":"On the Krull dimension of rings of semialgebraic functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.4109","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":"sha256:2d68e4e5d50cc6b3f78c3d8e88a7cd2770445005db1cc5a893d8697502991e6b","target":"record","created_at":"2026-05-18T03:20:37Z","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":"7926298ef2dbc42d800e52958df2d1dc927162bd14a44c7a7d23307128808ced","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-06-18T09:05:53Z","title_canon_sha256":"4f7e5be553d73ac004828bf3e3d605386861b4e5ed78cbe9c4c30d4b314cef02"},"schema_version":"1.0","source":{"id":"1306.4109","kind":"arxiv","version":1}},"canonical_sha256":"29c4961c9dfb857007201548e5972c4c3d45d0ebb236bf1de5f1a36a2cf2e649","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"29c4961c9dfb857007201548e5972c4c3d45d0ebb236bf1de5f1a36a2cf2e649","first_computed_at":"2026-05-18T03:20:37.131592Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:20:37.131592Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WCYPQGqO5noSwqUsUnlPDoozq5Fmf0/utQGXktEOX9P5RpCZ3u1MYb6G8jksXS9mL8++b9Ip3jHvaxaD6iRuCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:20:37.132294Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.4109","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d68e4e5d50cc6b3f78c3d8e88a7cd2770445005db1cc5a893d8697502991e6b","sha256:a6ae2b29c75d7da98cf0c3ecc946b544620dcfe4bc688d6ffbc12029ca19b532"],"state_sha256":"f71bba76caa5b6f4ebbe268ef218024586310e51c5c3aeb65e18a09891fb1513"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OJInHunpc8Vs21OYdGvu83N6syiTxlldzUomB2LsSuYbesVDoGYBB20MDL0MOodufE2DQ0k3skrwG80QZJi/BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T11:12:15.811112Z","bundle_sha256":"d7b495f440223e2295c4686760c7f891d4ea4583baa27d8118c6e2e49217bb22"}}