{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:744NP7KCB5XWVHMZE634ITWG5W","short_pith_number":"pith:744NP7KC","canonical_record":{"source":{"id":"1002.3562","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-02-18T16:18:48Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"5ce100b4a9b32b69d45aa75811ddc6ab4a2198f24d87cbd116e2d40965f52672","abstract_canon_sha256":"f6a554f8e9b3b8ae66b5e8089b1d8d64a2ac0eeb2e0b04f24242caa77032f2d0"},"schema_version":"1.0"},"canonical_sha256":"ff38d7fd420f6f6a9d9927b7c44ec6edb17a3241da91a59d0f2a7c55eeb3ada3","source":{"kind":"arxiv","id":"1002.3562","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.3562","created_at":"2026-05-18T04:30:12Z"},{"alias_kind":"arxiv_version","alias_value":"1002.3562v3","created_at":"2026-05-18T04:30:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.3562","created_at":"2026-05-18T04:30:12Z"},{"alias_kind":"pith_short_12","alias_value":"744NP7KCB5XW","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"744NP7KCB5XWVHMZ","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"744NP7KC","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:744NP7KCB5XWVHMZE634ITWG5W","target":"record","payload":{"canonical_record":{"source":{"id":"1002.3562","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-02-18T16:18:48Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"5ce100b4a9b32b69d45aa75811ddc6ab4a2198f24d87cbd116e2d40965f52672","abstract_canon_sha256":"f6a554f8e9b3b8ae66b5e8089b1d8d64a2ac0eeb2e0b04f24242caa77032f2d0"},"schema_version":"1.0"},"canonical_sha256":"ff38d7fd420f6f6a9d9927b7c44ec6edb17a3241da91a59d0f2a7c55eeb3ada3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:30:12.650207Z","signature_b64":"xlJWf7r3gf5cQzG4yJxT4xO1FFyamto7xvRL5+nhGXiuQ+N3P/HhR5H0adKnptPvu3YsNjcgvLp0WET/+hLYAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff38d7fd420f6f6a9d9927b7c44ec6edb17a3241da91a59d0f2a7c55eeb3ada3","last_reissued_at":"2026-05-18T04:30:12.649521Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:30:12.649521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1002.3562","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":"2026-05-18T04:30:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EERw5qq/Ihnn9FhBS8vC3kJPI83iTGd7m5e3g9UjrH+DUVxmhL35QGy0ABi3FCPWKslCv2BfpMEI7tLwDXm6DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:37:33.421157Z"},"content_sha256":"2c13a6203131fa9ef62bcf6a91619ed08ce3aaeda3c227e2731899752ef6a3ea","schema_version":"1.0","event_id":"sha256:2c13a6203131fa9ef62bcf6a91619ed08ce3aaeda3c227e2731899752ef6a3ea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:744NP7KCB5XWVHMZE634ITWG5W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algebraic geometry over algebraic structures II: Foundations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.AG","authors_text":"Alexei Myasnikov, Evelina Daniyarova, Vladimir Remeslennikov","submitted_at":"2010-02-18T16:18:48Z","abstract_excerpt":"In this paper we introduce elements of algebraic geometry over an arbitrary algebraic structure. We prove Unification Theorems which gather the description of coordinate algebras by several ways."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.3562","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":"2026-05-18T04:30:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yW1BoRsAM4y4srGGSbK+Hpvv/UyRSTm39CaMamtiAzjjDZ6m2sLni4mZiRmk6zEpGrabByNGqHfZxrx6Y4JOCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:37:33.421511Z"},"content_sha256":"8e85262b9b4b59ea2e2bbfab36e4bad24103cf1794b503139f14c47c09401f82","schema_version":"1.0","event_id":"sha256:8e85262b9b4b59ea2e2bbfab36e4bad24103cf1794b503139f14c47c09401f82"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/744NP7KCB5XWVHMZE634ITWG5W/bundle.json","state_url":"https://pith.science/pith/744NP7KCB5XWVHMZE634ITWG5W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/744NP7KCB5XWVHMZE634ITWG5W/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":"2026-06-03T16:37:33Z","links":{"resolver":"https://pith.science/pith/744NP7KCB5XWVHMZE634ITWG5W","bundle":"https://pith.science/pith/744NP7KCB5XWVHMZE634ITWG5W/bundle.json","state":"https://pith.science/pith/744NP7KCB5XWVHMZE634ITWG5W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/744NP7KCB5XWVHMZE634ITWG5W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:744NP7KCB5XWVHMZE634ITWG5W","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":"f6a554f8e9b3b8ae66b5e8089b1d8d64a2ac0eeb2e0b04f24242caa77032f2d0","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-02-18T16:18:48Z","title_canon_sha256":"5ce100b4a9b32b69d45aa75811ddc6ab4a2198f24d87cbd116e2d40965f52672"},"schema_version":"1.0","source":{"id":"1002.3562","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.3562","created_at":"2026-05-18T04:30:12Z"},{"alias_kind":"arxiv_version","alias_value":"1002.3562v3","created_at":"2026-05-18T04:30:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.3562","created_at":"2026-05-18T04:30:12Z"},{"alias_kind":"pith_short_12","alias_value":"744NP7KCB5XW","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"744NP7KCB5XWVHMZ","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"744NP7KC","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:8e85262b9b4b59ea2e2bbfab36e4bad24103cf1794b503139f14c47c09401f82","target":"graph","created_at":"2026-05-18T04:30:12Z","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":"In this paper we introduce elements of algebraic geometry over an arbitrary algebraic structure. We prove Unification Theorems which gather the description of coordinate algebras by several ways.","authors_text":"Alexei Myasnikov, Evelina Daniyarova, Vladimir Remeslennikov","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-02-18T16:18:48Z","title":"Algebraic geometry over algebraic structures II: Foundations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.3562","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":"sha256:2c13a6203131fa9ef62bcf6a91619ed08ce3aaeda3c227e2731899752ef6a3ea","target":"record","created_at":"2026-05-18T04:30:12Z","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":"f6a554f8e9b3b8ae66b5e8089b1d8d64a2ac0eeb2e0b04f24242caa77032f2d0","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-02-18T16:18:48Z","title_canon_sha256":"5ce100b4a9b32b69d45aa75811ddc6ab4a2198f24d87cbd116e2d40965f52672"},"schema_version":"1.0","source":{"id":"1002.3562","kind":"arxiv","version":3}},"canonical_sha256":"ff38d7fd420f6f6a9d9927b7c44ec6edb17a3241da91a59d0f2a7c55eeb3ada3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff38d7fd420f6f6a9d9927b7c44ec6edb17a3241da91a59d0f2a7c55eeb3ada3","first_computed_at":"2026-05-18T04:30:12.649521Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:30:12.649521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xlJWf7r3gf5cQzG4yJxT4xO1FFyamto7xvRL5+nhGXiuQ+N3P/HhR5H0adKnptPvu3YsNjcgvLp0WET/+hLYAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:30:12.650207Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.3562","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2c13a6203131fa9ef62bcf6a91619ed08ce3aaeda3c227e2731899752ef6a3ea","sha256:8e85262b9b4b59ea2e2bbfab36e4bad24103cf1794b503139f14c47c09401f82"],"state_sha256":"f6014983d58212d7e78ebeecdf33d422811c90923bf4c82d4b481ce34410a279"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QskevANi8o5ukrMh7K/abdXP6+pcGYcbjkoCuxUL+BDNHGfqlZExPMQjn6lNIPiBiddfF4P3M5eTxuFBBjIDAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T16:37:33.423485Z","bundle_sha256":"62952dd04be7d261b517cb5aaf3a927a1b6c53f14500926fab9bbeb8a9a1e8a4"}}