{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:ID2TXHYY4XMT6A3BCVO5OWYLZ2","short_pith_number":"pith:ID2TXHYY","canonical_record":{"source":{"id":"1005.0171","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-05-02T22:19:10Z","cross_cats_sorted":[],"title_canon_sha256":"ed04e9d15c3d39d414763be208d6f6258a76b371bb2346da1283b45676301c2b","abstract_canon_sha256":"2fdd66bd6bf28c32b695f0d7fab2868ae79f6d81e63d9f89b022ba1788150197"},"schema_version":"1.0"},"canonical_sha256":"40f53b9f18e5d93f0361155dd75b0bcebab01c8899f9ccafeca86b99b4fc9e78","source":{"kind":"arxiv","id":"1005.0171","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.0171","created_at":"2026-05-18T02:07:43Z"},{"alias_kind":"arxiv_version","alias_value":"1005.0171v1","created_at":"2026-05-18T02:07:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.0171","created_at":"2026-05-18T02:07:43Z"},{"alias_kind":"pith_short_12","alias_value":"ID2TXHYY4XMT","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"ID2TXHYY4XMT6A3B","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"ID2TXHYY","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:ID2TXHYY4XMT6A3BCVO5OWYLZ2","target":"record","payload":{"canonical_record":{"source":{"id":"1005.0171","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-05-02T22:19:10Z","cross_cats_sorted":[],"title_canon_sha256":"ed04e9d15c3d39d414763be208d6f6258a76b371bb2346da1283b45676301c2b","abstract_canon_sha256":"2fdd66bd6bf28c32b695f0d7fab2868ae79f6d81e63d9f89b022ba1788150197"},"schema_version":"1.0"},"canonical_sha256":"40f53b9f18e5d93f0361155dd75b0bcebab01c8899f9ccafeca86b99b4fc9e78","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:07:43.938091Z","signature_b64":"YYNg9hrDlu+rHLmjubo7hTNKDwZUqAMiTh24ueDQgnoZ7oXoTVStT0BiKU5JoMVv1LhFpN+yacAtXmqpjDA4Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"40f53b9f18e5d93f0361155dd75b0bcebab01c8899f9ccafeca86b99b4fc9e78","last_reissued_at":"2026-05-18T02:07:43.937339Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:07:43.937339Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1005.0171","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":"2026-05-18T02:07:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aElaGxAymgeWe53DTyUx9/muzM/ToyR133XouJH3etpVe2g+uBXwM+YYMJwU/kJtEucz0wnhMmWyTakKyzK9Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T00:22:12.807780Z"},"content_sha256":"df7cd7456d306ff6f4e5ce80b0612817d0895382d5a31ea8a5059472d0c928c5","schema_version":"1.0","event_id":"sha256:df7cd7456d306ff6f4e5ce80b0612817d0895382d5a31ea8a5059472d0c928c5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:ID2TXHYY4XMT6A3BCVO5OWYLZ2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Every State on Interval Effect Algebra is Integral","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Anatolij Dvure\\v{c}enskij","submitted_at":"2010-05-02T22:19:10Z","abstract_excerpt":"We show that every state on an interval effect algebra is an integral through some regular Borel probability measure defined on the Borel $\\sigma$-algebra of a compact Hausdorff simplex. This is true for every effect algebra satisfying (RDP) or for every  MV-algebra. In addition, we show that each state on an effect subalgebra of an interval effect algebra $E$ can be extended to a state on $E.$ Our method represents also every state on the set of  effect operators of a Hilbert space as an integral"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.0171","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":"2026-05-18T02:07:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zfaeAYBsTifK+pPYiqM9Mu/XOU9ozqH/5k49GqDa+2z5wGaBJHwziDHXS/EXCsklOY8rnYuEuawnwT0EtJLwAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T00:22:12.808116Z"},"content_sha256":"6f9b91b15925134093d9f6c092e84015a09881d6cf8c385fc10f6095c8f62b9b","schema_version":"1.0","event_id":"sha256:6f9b91b15925134093d9f6c092e84015a09881d6cf8c385fc10f6095c8f62b9b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ID2TXHYY4XMT6A3BCVO5OWYLZ2/bundle.json","state_url":"https://pith.science/pith/ID2TXHYY4XMT6A3BCVO5OWYLZ2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ID2TXHYY4XMT6A3BCVO5OWYLZ2/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":"2026-06-03T00:22:12Z","links":{"resolver":"https://pith.science/pith/ID2TXHYY4XMT6A3BCVO5OWYLZ2","bundle":"https://pith.science/pith/ID2TXHYY4XMT6A3BCVO5OWYLZ2/bundle.json","state":"https://pith.science/pith/ID2TXHYY4XMT6A3BCVO5OWYLZ2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ID2TXHYY4XMT6A3BCVO5OWYLZ2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:ID2TXHYY4XMT6A3BCVO5OWYLZ2","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":"2fdd66bd6bf28c32b695f0d7fab2868ae79f6d81e63d9f89b022ba1788150197","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-05-02T22:19:10Z","title_canon_sha256":"ed04e9d15c3d39d414763be208d6f6258a76b371bb2346da1283b45676301c2b"},"schema_version":"1.0","source":{"id":"1005.0171","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.0171","created_at":"2026-05-18T02:07:43Z"},{"alias_kind":"arxiv_version","alias_value":"1005.0171v1","created_at":"2026-05-18T02:07:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.0171","created_at":"2026-05-18T02:07:43Z"},{"alias_kind":"pith_short_12","alias_value":"ID2TXHYY4XMT","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"ID2TXHYY4XMT6A3B","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"ID2TXHYY","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:6f9b91b15925134093d9f6c092e84015a09881d6cf8c385fc10f6095c8f62b9b","target":"graph","created_at":"2026-05-18T02:07:43Z","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 every state on an interval effect algebra is an integral through some regular Borel probability measure defined on the Borel $\\sigma$-algebra of a compact Hausdorff simplex. This is true for every effect algebra satisfying (RDP) or for every  MV-algebra. In addition, we show that each state on an effect subalgebra of an interval effect algebra $E$ can be extended to a state on $E.$ Our method represents also every state on the set of  effect operators of a Hilbert space as an integral","authors_text":"Anatolij Dvure\\v{c}enskij","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-05-02T22:19:10Z","title":"Every State on Interval Effect Algebra is Integral"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.0171","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:df7cd7456d306ff6f4e5ce80b0612817d0895382d5a31ea8a5059472d0c928c5","target":"record","created_at":"2026-05-18T02:07:43Z","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":"2fdd66bd6bf28c32b695f0d7fab2868ae79f6d81e63d9f89b022ba1788150197","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-05-02T22:19:10Z","title_canon_sha256":"ed04e9d15c3d39d414763be208d6f6258a76b371bb2346da1283b45676301c2b"},"schema_version":"1.0","source":{"id":"1005.0171","kind":"arxiv","version":1}},"canonical_sha256":"40f53b9f18e5d93f0361155dd75b0bcebab01c8899f9ccafeca86b99b4fc9e78","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"40f53b9f18e5d93f0361155dd75b0bcebab01c8899f9ccafeca86b99b4fc9e78","first_computed_at":"2026-05-18T02:07:43.937339Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:07:43.937339Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YYNg9hrDlu+rHLmjubo7hTNKDwZUqAMiTh24ueDQgnoZ7oXoTVStT0BiKU5JoMVv1LhFpN+yacAtXmqpjDA4Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:07:43.938091Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.0171","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:df7cd7456d306ff6f4e5ce80b0612817d0895382d5a31ea8a5059472d0c928c5","sha256:6f9b91b15925134093d9f6c092e84015a09881d6cf8c385fc10f6095c8f62b9b"],"state_sha256":"a3ee26b457e32151a6c58fc26daf8ecfba05a92de5ae78219b20a12cb84b1337"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wKrIWHPZ+VFME1BvbTaHkpTLBhXYucHblSBzlulVX34edSiLj0IWJCYcBFukUUxewmYy8Fw1M6gpdPg7xVNnCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T00:22:12.810012Z","bundle_sha256":"8a6f32642897d010395df1d9dd605bbcf334f4d21bfe1f9e612a883204384f31"}}