{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:HA5QSNUEGMVY6TWKPYXYVTVX7Z","short_pith_number":"pith:HA5QSNUE","canonical_record":{"source":{"id":"1708.06091","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-08-21T06:50:17Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"c0317212a5601a3e4ed5906ae228876f72ae013348ecba512ddb0378eccec779","abstract_canon_sha256":"ffcfc4322bb385ec8efaaef55c200ff3bf3607f819a4d8e4b7fcc3390030c1b8"},"schema_version":"1.0"},"canonical_sha256":"383b093684332b8f4eca7e2f8aceb7fe794245b055bd7071568639b01867c646","source":{"kind":"arxiv","id":"1708.06091","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.06091","created_at":"2026-05-18T00:35:03Z"},{"alias_kind":"arxiv_version","alias_value":"1708.06091v1","created_at":"2026-05-18T00:35:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.06091","created_at":"2026-05-18T00:35:03Z"},{"alias_kind":"pith_short_12","alias_value":"HA5QSNUEGMVY","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"HA5QSNUEGMVY6TWK","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"HA5QSNUE","created_at":"2026-05-18T12:31:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:HA5QSNUEGMVY6TWKPYXYVTVX7Z","target":"record","payload":{"canonical_record":{"source":{"id":"1708.06091","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-08-21T06:50:17Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"c0317212a5601a3e4ed5906ae228876f72ae013348ecba512ddb0378eccec779","abstract_canon_sha256":"ffcfc4322bb385ec8efaaef55c200ff3bf3607f819a4d8e4b7fcc3390030c1b8"},"schema_version":"1.0"},"canonical_sha256":"383b093684332b8f4eca7e2f8aceb7fe794245b055bd7071568639b01867c646","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:03.638244Z","signature_b64":"YMvFhJxD730x+Qj2Aq/obCUTAZqJB6pKokq6qoXd9Cvr3rI8Uf0KuTaSW7YZ+UyqS7cMO1krXjLG1hzXt0e8DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"383b093684332b8f4eca7e2f8aceb7fe794245b055bd7071568639b01867c646","last_reissued_at":"2026-05-18T00:35:03.637531Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:03.637531Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.06091","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":"2026-05-18T00:35:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e22IfVwc/+Ey02mS/y4W6TL96WrKcaUH7nCFhedBoC6AnvKHV7MArXWEQb33sR9BbBWU+ggfPffcjJQnbpZBBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T22:25:57.151182Z"},"content_sha256":"dba0764d1dfd39f5df773797325fd8afb7743bada752a2039a0364ed7622d856","schema_version":"1.0","event_id":"sha256:dba0764d1dfd39f5df773797325fd8afb7743bada752a2039a0364ed7622d856"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:HA5QSNUEGMVY6TWKPYXYVTVX7Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"States on EMV-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.LO","authors_text":"Anatolij Dvure\\v{c}enskij, Omid Zahiri","submitted_at":"2017-08-21T06:50:17Z","abstract_excerpt":"We define a state as a $[0,1]$-valued, finitely additive function attaining the value $1$ on an EMV-algebra, which is an algebraic structure close to MV-algebras, where the top element is not assumed. We show that states always exist, the extremal states are exactly state-morphisms. Nevertheless the state space is a convex space that is not necessarily compact, a variant of the Krein--Mil'man theorem saying states are generated by extremal states, is proved. We define a weaker form of states, pre-states and strong pre-states, and also Jordan signed measures which form a Dedekind complete $\\ell"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.06091","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":"2026-05-18T00:35:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XssEg4Yb5sswyf3UOoK38U5PPgXv9HJ6PxLOllvueGwf14N+TEzYd/wm7u/tHr+ZBkgG+/1frdiTbHJBpUx7Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T22:25:57.151543Z"},"content_sha256":"0dff20614b2f919b766f96df872a1377c1d3e6006116bcde24a1ef2fa8f1b4fb","schema_version":"1.0","event_id":"sha256:0dff20614b2f919b766f96df872a1377c1d3e6006116bcde24a1ef2fa8f1b4fb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HA5QSNUEGMVY6TWKPYXYVTVX7Z/bundle.json","state_url":"https://pith.science/pith/HA5QSNUEGMVY6TWKPYXYVTVX7Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HA5QSNUEGMVY6TWKPYXYVTVX7Z/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":"2026-06-02T22:25:57Z","links":{"resolver":"https://pith.science/pith/HA5QSNUEGMVY6TWKPYXYVTVX7Z","bundle":"https://pith.science/pith/HA5QSNUEGMVY6TWKPYXYVTVX7Z/bundle.json","state":"https://pith.science/pith/HA5QSNUEGMVY6TWKPYXYVTVX7Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HA5QSNUEGMVY6TWKPYXYVTVX7Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:HA5QSNUEGMVY6TWKPYXYVTVX7Z","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":"ffcfc4322bb385ec8efaaef55c200ff3bf3607f819a4d8e4b7fcc3390030c1b8","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-08-21T06:50:17Z","title_canon_sha256":"c0317212a5601a3e4ed5906ae228876f72ae013348ecba512ddb0378eccec779"},"schema_version":"1.0","source":{"id":"1708.06091","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.06091","created_at":"2026-05-18T00:35:03Z"},{"alias_kind":"arxiv_version","alias_value":"1708.06091v1","created_at":"2026-05-18T00:35:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.06091","created_at":"2026-05-18T00:35:03Z"},{"alias_kind":"pith_short_12","alias_value":"HA5QSNUEGMVY","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"HA5QSNUEGMVY6TWK","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"HA5QSNUE","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:0dff20614b2f919b766f96df872a1377c1d3e6006116bcde24a1ef2fa8f1b4fb","target":"graph","created_at":"2026-05-18T00:35:03Z","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 define a state as a $[0,1]$-valued, finitely additive function attaining the value $1$ on an EMV-algebra, which is an algebraic structure close to MV-algebras, where the top element is not assumed. We show that states always exist, the extremal states are exactly state-morphisms. Nevertheless the state space is a convex space that is not necessarily compact, a variant of the Krein--Mil'man theorem saying states are generated by extremal states, is proved. We define a weaker form of states, pre-states and strong pre-states, and also Jordan signed measures which form a Dedekind complete $\\ell","authors_text":"Anatolij Dvure\\v{c}enskij, Omid Zahiri","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-08-21T06:50:17Z","title":"States on EMV-algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.06091","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:dba0764d1dfd39f5df773797325fd8afb7743bada752a2039a0364ed7622d856","target":"record","created_at":"2026-05-18T00:35:03Z","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":"ffcfc4322bb385ec8efaaef55c200ff3bf3607f819a4d8e4b7fcc3390030c1b8","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-08-21T06:50:17Z","title_canon_sha256":"c0317212a5601a3e4ed5906ae228876f72ae013348ecba512ddb0378eccec779"},"schema_version":"1.0","source":{"id":"1708.06091","kind":"arxiv","version":1}},"canonical_sha256":"383b093684332b8f4eca7e2f8aceb7fe794245b055bd7071568639b01867c646","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"383b093684332b8f4eca7e2f8aceb7fe794245b055bd7071568639b01867c646","first_computed_at":"2026-05-18T00:35:03.637531Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:03.637531Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YMvFhJxD730x+Qj2Aq/obCUTAZqJB6pKokq6qoXd9Cvr3rI8Uf0KuTaSW7YZ+UyqS7cMO1krXjLG1hzXt0e8DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:03.638244Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.06091","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dba0764d1dfd39f5df773797325fd8afb7743bada752a2039a0364ed7622d856","sha256:0dff20614b2f919b766f96df872a1377c1d3e6006116bcde24a1ef2fa8f1b4fb"],"state_sha256":"d59793fc571afa1d56102030063c1980940cd9914fb9fb2922c6dc62b02b8cdb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xpHqhfj9M62c/rsj8xQNL2zvodrAYBVXBxneOIqBBn6gzVGCKZLPZH6zH9QYk7N8hUnF5UCKEpUX4R0AjUL6BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T22:25:57.153461Z","bundle_sha256":"c627cbc190820b2ff7e6be0955bf5a7254cbb02ea0ff557e0906eebab3a09a52"}}