{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:FLF3NJL5DGKGJKHJA7NT6DPY65","short_pith_number":"pith:FLF3NJL5","canonical_record":{"source":{"id":"1610.09268","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-10-28T15:26:55Z","cross_cats_sorted":[],"title_canon_sha256":"ba1895986a5c552e40150a3e77face36a79b82d175c5769ea965de3f58144dbf","abstract_canon_sha256":"877747a75859d8183f73793958532c7cc2a7429dfa7d4923e599b4310d2c03bc"},"schema_version":"1.0"},"canonical_sha256":"2acbb6a57d199464a8e907db3f0df8f7580f4f55aae2410e182008824088f257","source":{"kind":"arxiv","id":"1610.09268","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.09268","created_at":"2026-05-17T23:40:14Z"},{"alias_kind":"arxiv_version","alias_value":"1610.09268v3","created_at":"2026-05-17T23:40:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09268","created_at":"2026-05-17T23:40:14Z"},{"alias_kind":"pith_short_12","alias_value":"FLF3NJL5DGKG","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FLF3NJL5DGKGJKHJ","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FLF3NJL5","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:FLF3NJL5DGKGJKHJA7NT6DPY65","target":"record","payload":{"canonical_record":{"source":{"id":"1610.09268","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-10-28T15:26:55Z","cross_cats_sorted":[],"title_canon_sha256":"ba1895986a5c552e40150a3e77face36a79b82d175c5769ea965de3f58144dbf","abstract_canon_sha256":"877747a75859d8183f73793958532c7cc2a7429dfa7d4923e599b4310d2c03bc"},"schema_version":"1.0"},"canonical_sha256":"2acbb6a57d199464a8e907db3f0df8f7580f4f55aae2410e182008824088f257","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:14.544448Z","signature_b64":"Yz1MCTJu1J2mvAt6/7FLD9DHwr8foJNzknZbuu0V3C5yabEUD1ByFhJLEgBbk/rBRXst3x1tlA+JmQbf45hvCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2acbb6a57d199464a8e907db3f0df8f7580f4f55aae2410e182008824088f257","last_reissued_at":"2026-05-17T23:40:14.543747Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:14.543747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.09268","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:40:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8hEeyGqp3lP3yCnZA+r9q3TFqgkUdso6UDpVDubLgl/cqjLrWCDyFfEWZky+gBceWfHqI0in3iyU3ilEbUt7Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T00:44:23.164111Z"},"content_sha256":"8a6fb33bf97215a2501e7f1806112ab5ae5de9ace3756382cc5b6a90c92eeb4e","schema_version":"1.0","event_id":"sha256:8a6fb33bf97215a2501e7f1806112ab5ae5de9ace3756382cc5b6a90c92eeb4e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:FLF3NJL5DGKGJKHJA7NT6DPY65","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Small Subalgebras of Polynomial Rings and Stillman's Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Melvin Hochster, Tigran Ananyan","submitted_at":"2016-10-28T15:26:55Z","abstract_excerpt":"We show that in a polynomial ring $R$ in $N$ variables over an algebraically closed field $K$ of arbitrary characteristic, any $K$-subalgebra of $R$ generated over $K$ by at most $n$ forms of degree at most $d$ is contained in a $K$-subalgebra of $R$ generated by $B \\leq {}^\\eta\\mathcal{B}(n,d)$ forms $G_1,..., G_B$ of degree $\\leq d$, where ${}^\\eta\\mathcal{B}(n,d)$ does not depend on $N$ or $K$, such that these forms are a regular sequence and such that for any ideal $J$ generated by forms that are in the $K$-span of $G_1, ..., G_B$, the ring $R/J$ satisfies the Serre condition $R_\\eta$. The"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09268","kind":"arxiv","version":3},"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":"2026-05-17T23:40:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ArPG2GXSUucWgNRy+6TLKFEooLh1Ue/ePT+24ry8HzfcxVTeZ3oZDlyOjM7ij+Y11hXJbHx/JMF81AZQzKV5Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T00:44:23.164475Z"},"content_sha256":"449ac29689debbdd5bb700dd91f98ece284bc5aff2392576321672364e4194b1","schema_version":"1.0","event_id":"sha256:449ac29689debbdd5bb700dd91f98ece284bc5aff2392576321672364e4194b1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FLF3NJL5DGKGJKHJA7NT6DPY65/bundle.json","state_url":"https://pith.science/pith/FLF3NJL5DGKGJKHJA7NT6DPY65/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FLF3NJL5DGKGJKHJA7NT6DPY65/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":"2026-06-02T00:44:23Z","links":{"resolver":"https://pith.science/pith/FLF3NJL5DGKGJKHJA7NT6DPY65","bundle":"https://pith.science/pith/FLF3NJL5DGKGJKHJA7NT6DPY65/bundle.json","state":"https://pith.science/pith/FLF3NJL5DGKGJKHJA7NT6DPY65/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FLF3NJL5DGKGJKHJA7NT6DPY65/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:FLF3NJL5DGKGJKHJA7NT6DPY65","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":"877747a75859d8183f73793958532c7cc2a7429dfa7d4923e599b4310d2c03bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-10-28T15:26:55Z","title_canon_sha256":"ba1895986a5c552e40150a3e77face36a79b82d175c5769ea965de3f58144dbf"},"schema_version":"1.0","source":{"id":"1610.09268","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.09268","created_at":"2026-05-17T23:40:14Z"},{"alias_kind":"arxiv_version","alias_value":"1610.09268v3","created_at":"2026-05-17T23:40:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09268","created_at":"2026-05-17T23:40:14Z"},{"alias_kind":"pith_short_12","alias_value":"FLF3NJL5DGKG","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FLF3NJL5DGKGJKHJ","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FLF3NJL5","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:449ac29689debbdd5bb700dd91f98ece284bc5aff2392576321672364e4194b1","target":"graph","created_at":"2026-05-17T23:40:14Z","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 show that in a polynomial ring $R$ in $N$ variables over an algebraically closed field $K$ of arbitrary characteristic, any $K$-subalgebra of $R$ generated over $K$ by at most $n$ forms of degree at most $d$ is contained in a $K$-subalgebra of $R$ generated by $B \\leq {}^\\eta\\mathcal{B}(n,d)$ forms $G_1,..., G_B$ of degree $\\leq d$, where ${}^\\eta\\mathcal{B}(n,d)$ does not depend on $N$ or $K$, such that these forms are a regular sequence and such that for any ideal $J$ generated by forms that are in the $K$-span of $G_1, ..., G_B$, the ring $R/J$ satisfies the Serre condition $R_\\eta$. The","authors_text":"Melvin Hochster, Tigran Ananyan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-10-28T15:26:55Z","title":"Small Subalgebras of Polynomial Rings and Stillman's Conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09268","kind":"arxiv","version":3},"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":"sha256:8a6fb33bf97215a2501e7f1806112ab5ae5de9ace3756382cc5b6a90c92eeb4e","target":"record","created_at":"2026-05-17T23:40:14Z","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":"877747a75859d8183f73793958532c7cc2a7429dfa7d4923e599b4310d2c03bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-10-28T15:26:55Z","title_canon_sha256":"ba1895986a5c552e40150a3e77face36a79b82d175c5769ea965de3f58144dbf"},"schema_version":"1.0","source":{"id":"1610.09268","kind":"arxiv","version":3}},"canonical_sha256":"2acbb6a57d199464a8e907db3f0df8f7580f4f55aae2410e182008824088f257","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2acbb6a57d199464a8e907db3f0df8f7580f4f55aae2410e182008824088f257","first_computed_at":"2026-05-17T23:40:14.543747Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:14.543747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Yz1MCTJu1J2mvAt6/7FLD9DHwr8foJNzknZbuu0V3C5yabEUD1ByFhJLEgBbk/rBRXst3x1tlA+JmQbf45hvCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:14.544448Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.09268","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a6fb33bf97215a2501e7f1806112ab5ae5de9ace3756382cc5b6a90c92eeb4e","sha256:449ac29689debbdd5bb700dd91f98ece284bc5aff2392576321672364e4194b1"],"state_sha256":"ed9f991a3e7c0019eb9b1c4ed2ccaafa5bd2b3f3296594712c222cd4eaa08c15"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RZfL3LgdIWzza5RTdbxbTlw5kNg2la19Nva18CGQJsmRe4SpJ+GBWJZDfeuYxKIugXCEwZ8d7TrGHgisJHikCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T00:44:23.166439Z","bundle_sha256":"2e7d8d3a53e28b627a167c54080ece451a5028dc4771e58b59fc11d5d9e28079"}}