{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:NNUG7ET2AJW2AOROTIU5RYCQXT","short_pith_number":"pith:NNUG7ET2","canonical_record":{"source":{"id":"0803.3969","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2008-03-27T16:01:31Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"f4db392ebed3b60afa1761defca257ec3e9f775572e12dcd447a12c1c60e2d66","abstract_canon_sha256":"f72779df312620a36024f7b5ba9250e5dc242569f5c5ca1b53b1cea031f15711"},"schema_version":"1.0"},"canonical_sha256":"6b686f927a026da03a2e9a29d8e050bcd1acb20e31f58445b7ae802d99a599a2","source":{"kind":"arxiv","id":"0803.3969","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0803.3969","created_at":"2026-05-18T03:25:14Z"},{"alias_kind":"arxiv_version","alias_value":"0803.3969v3","created_at":"2026-05-18T03:25:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0803.3969","created_at":"2026-05-18T03:25:14Z"},{"alias_kind":"pith_short_12","alias_value":"NNUG7ET2AJW2","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"NNUG7ET2AJW2AORO","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"NNUG7ET2","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:NNUG7ET2AJW2AOROTIU5RYCQXT","target":"record","payload":{"canonical_record":{"source":{"id":"0803.3969","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2008-03-27T16:01:31Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"f4db392ebed3b60afa1761defca257ec3e9f775572e12dcd447a12c1c60e2d66","abstract_canon_sha256":"f72779df312620a36024f7b5ba9250e5dc242569f5c5ca1b53b1cea031f15711"},"schema_version":"1.0"},"canonical_sha256":"6b686f927a026da03a2e9a29d8e050bcd1acb20e31f58445b7ae802d99a599a2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:14.913902Z","signature_b64":"etuGEmxKpHfTX20vGUsjiSNXIo7xMvdB9MHFmKlrrlmDySp8TZeYXVMjnk9gAxEYBzPey3ShP7s6q5ktWkRUDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b686f927a026da03a2e9a29d8e050bcd1acb20e31f58445b7ae802d99a599a2","last_reissued_at":"2026-05-18T03:25:14.913322Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:14.913322Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0803.3969","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":"2026-05-18T03:25:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YOKgpa8tT+JbYUlsV/7gH7UU1FWPTu1HJm73RIPPmiskGilIGZJ22OLWft9xQ8DmyCYc060ArpxSTJpvmiW/Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T08:37:06.703739Z"},"content_sha256":"4b2ff9b97772f056f03c1bba250a7314965bbeba8d90ef60ae2670f09c71b18a","schema_version":"1.0","event_id":"sha256:4b2ff9b97772f056f03c1bba250a7314965bbeba8d90ef60ae2670f09c71b18a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:NNUG7ET2AJW2AOROTIU5RYCQXT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cancellation Meadows: a Generic Basis Theorem and Some Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"math.RA","authors_text":"Alban Ponse, Inge Bethke, Jan A. Bergstra","submitted_at":"2008-03-27T16:01:31Z","abstract_excerpt":"Let Q_0 denote the rational numbers expanded to a \"meadow\", that is, after taking its zero-totalized form (0^{-1}=0) as the preferred interpretation. In this paper we consider \"cancellation meadows\", i.e., meadows without proper zero divisors, such as $Q_0$ and prove a generic completeness result. We apply this result to cancellation meadows expanded with differentiation operators, the sign function, and with floor, ceiling and a signed variant of the square root, respectively. We give an equational axiomatization of these operators and thus obtain a finite basis for various expanded cancellat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0803.3969","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":"2026-05-18T03:25:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iJI12iSc1LFTJgnaNnLqHG1m3haEMZfZizzh/tHOp8jbbkVpIPq1OFqMVGzQXyojpSiKxo1sWFWJgAA1E1HAAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T08:37:06.704105Z"},"content_sha256":"96555b397fcbcd392dcc15bc2d989ab418967021bc5ac3bea310b34f6eef47cd","schema_version":"1.0","event_id":"sha256:96555b397fcbcd392dcc15bc2d989ab418967021bc5ac3bea310b34f6eef47cd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NNUG7ET2AJW2AOROTIU5RYCQXT/bundle.json","state_url":"https://pith.science/pith/NNUG7ET2AJW2AOROTIU5RYCQXT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NNUG7ET2AJW2AOROTIU5RYCQXT/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":"2026-06-03T08:37:06Z","links":{"resolver":"https://pith.science/pith/NNUG7ET2AJW2AOROTIU5RYCQXT","bundle":"https://pith.science/pith/NNUG7ET2AJW2AOROTIU5RYCQXT/bundle.json","state":"https://pith.science/pith/NNUG7ET2AJW2AOROTIU5RYCQXT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NNUG7ET2AJW2AOROTIU5RYCQXT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:NNUG7ET2AJW2AOROTIU5RYCQXT","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":"f72779df312620a36024f7b5ba9250e5dc242569f5c5ca1b53b1cea031f15711","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2008-03-27T16:01:31Z","title_canon_sha256":"f4db392ebed3b60afa1761defca257ec3e9f775572e12dcd447a12c1c60e2d66"},"schema_version":"1.0","source":{"id":"0803.3969","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0803.3969","created_at":"2026-05-18T03:25:14Z"},{"alias_kind":"arxiv_version","alias_value":"0803.3969v3","created_at":"2026-05-18T03:25:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0803.3969","created_at":"2026-05-18T03:25:14Z"},{"alias_kind":"pith_short_12","alias_value":"NNUG7ET2AJW2","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"NNUG7ET2AJW2AORO","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"NNUG7ET2","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:96555b397fcbcd392dcc15bc2d989ab418967021bc5ac3bea310b34f6eef47cd","target":"graph","created_at":"2026-05-18T03:25:14Z","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":"Let Q_0 denote the rational numbers expanded to a \"meadow\", that is, after taking its zero-totalized form (0^{-1}=0) as the preferred interpretation. In this paper we consider \"cancellation meadows\", i.e., meadows without proper zero divisors, such as $Q_0$ and prove a generic completeness result. We apply this result to cancellation meadows expanded with differentiation operators, the sign function, and with floor, ceiling and a signed variant of the square root, respectively. We give an equational axiomatization of these operators and thus obtain a finite basis for various expanded cancellat","authors_text":"Alban Ponse, Inge Bethke, Jan A. Bergstra","cross_cats":["cs.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2008-03-27T16:01:31Z","title":"Cancellation Meadows: a Generic Basis Theorem and Some Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0803.3969","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":"sha256:4b2ff9b97772f056f03c1bba250a7314965bbeba8d90ef60ae2670f09c71b18a","target":"record","created_at":"2026-05-18T03:25:14Z","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":"f72779df312620a36024f7b5ba9250e5dc242569f5c5ca1b53b1cea031f15711","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2008-03-27T16:01:31Z","title_canon_sha256":"f4db392ebed3b60afa1761defca257ec3e9f775572e12dcd447a12c1c60e2d66"},"schema_version":"1.0","source":{"id":"0803.3969","kind":"arxiv","version":3}},"canonical_sha256":"6b686f927a026da03a2e9a29d8e050bcd1acb20e31f58445b7ae802d99a599a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b686f927a026da03a2e9a29d8e050bcd1acb20e31f58445b7ae802d99a599a2","first_computed_at":"2026-05-18T03:25:14.913322Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:25:14.913322Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"etuGEmxKpHfTX20vGUsjiSNXIo7xMvdB9MHFmKlrrlmDySp8TZeYXVMjnk9gAxEYBzPey3ShP7s6q5ktWkRUDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:25:14.913902Z","signed_message":"canonical_sha256_bytes"},"source_id":"0803.3969","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b2ff9b97772f056f03c1bba250a7314965bbeba8d90ef60ae2670f09c71b18a","sha256:96555b397fcbcd392dcc15bc2d989ab418967021bc5ac3bea310b34f6eef47cd"],"state_sha256":"ae4f3030d8c260f80df3f815698d3e78bbc6b1d2223dd126ff6e252c59262aa0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j7c2Kv0QJV39yVEabT9TDemEZDQeFj9RU7eppvR2koOdkP0kWHUBTzJZd+aBtcR535qxTBfC6mvceLSRn3VPDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T08:37:06.706181Z","bundle_sha256":"8881dfc69088dd9db492c3a6b8c3943bfe68baa85de749c6604ff65b01017976"}}