{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:IJ3SDNCIFZB6IUPQFCOMTQZPI6","short_pith_number":"pith:IJ3SDNCI","canonical_record":{"source":{"id":"1204.0605","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-04-03T06:32:04Z","cross_cats_sorted":[],"title_canon_sha256":"ce1455d06c4ebb6d7041083bf63e711413a2c84af2fdc66ca94a55d9269e334b","abstract_canon_sha256":"b4df8991be0350f10233f3a71abb1de2ab5e68c7815ecdc4a9819fc7cc53b411"},"schema_version":"1.0"},"canonical_sha256":"427721b4482e43e451f0289cc9c32f479522f7fa00a80e98a52194220cb82e74","source":{"kind":"arxiv","id":"1204.0605","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.0605","created_at":"2026-05-18T03:58:39Z"},{"alias_kind":"arxiv_version","alias_value":"1204.0605v1","created_at":"2026-05-18T03:58:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.0605","created_at":"2026-05-18T03:58:39Z"},{"alias_kind":"pith_short_12","alias_value":"IJ3SDNCIFZB6","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IJ3SDNCIFZB6IUPQ","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IJ3SDNCI","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:IJ3SDNCIFZB6IUPQFCOMTQZPI6","target":"record","payload":{"canonical_record":{"source":{"id":"1204.0605","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-04-03T06:32:04Z","cross_cats_sorted":[],"title_canon_sha256":"ce1455d06c4ebb6d7041083bf63e711413a2c84af2fdc66ca94a55d9269e334b","abstract_canon_sha256":"b4df8991be0350f10233f3a71abb1de2ab5e68c7815ecdc4a9819fc7cc53b411"},"schema_version":"1.0"},"canonical_sha256":"427721b4482e43e451f0289cc9c32f479522f7fa00a80e98a52194220cb82e74","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:58:39.027258Z","signature_b64":"P0W9JgkeycKskktTtbtrjPCboRThsbk5kxpUgH+5Qo51tPyDNCPzwW0OWcIw0nXwlLQZDs6+EID5bBClK5diBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"427721b4482e43e451f0289cc9c32f479522f7fa00a80e98a52194220cb82e74","last_reissued_at":"2026-05-18T03:58:39.026670Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:58:39.026670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.0605","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":"2026-05-18T03:58:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DrqI8B6J/0CTHW3Usjz2G5YHxtnWm6lMaovPoOpoS0eJ9wz9PA8yGyzoKqlGhRnywPwE2y0fDidtMhgUwaTgBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T11:44:28.482955Z"},"content_sha256":"ad0abe42e0897ce52336a33efdf14c880a0c74e0682536430a0643cebafeccea","schema_version":"1.0","event_id":"sha256:ad0abe42e0897ce52336a33efdf14c880a0c74e0682536430a0643cebafeccea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:IJ3SDNCIFZB6IUPQFCOMTQZPI6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Triple Representation Theorem for homogeneous effect algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Jan Paseka, Josef Niederle","submitted_at":"2012-04-03T06:32:04Z","abstract_excerpt":"The aim of our paper is to prove the Triple Representation Theorem, which was established by Jen\\v{c}a in the setting of complete lattice effect algebras, for a special class of homogeneous effect algebras, namely TRT-effect algebras. This class includes complete lattice effect algebras, sharply dominating Archimedean atomic lattice effect algebras and homogeneous orthocomplete effect algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.0605","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":"2026-05-18T03:58:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C3gGu33AGveYPpDrvqQJRk23J7hfDU5Y5yZp51DcmTWSsZjn7lnEx7aY9iYzIZLwSxeuUV8lxPq89M9qBLXhDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T11:44:28.483573Z"},"content_sha256":"0469d8f19533ca72808b8817d42aadc4893634aea6b41547c503bf2ac35e36d8","schema_version":"1.0","event_id":"sha256:0469d8f19533ca72808b8817d42aadc4893634aea6b41547c503bf2ac35e36d8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IJ3SDNCIFZB6IUPQFCOMTQZPI6/bundle.json","state_url":"https://pith.science/pith/IJ3SDNCIFZB6IUPQFCOMTQZPI6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IJ3SDNCIFZB6IUPQFCOMTQZPI6/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":"2026-06-10T11:44:28Z","links":{"resolver":"https://pith.science/pith/IJ3SDNCIFZB6IUPQFCOMTQZPI6","bundle":"https://pith.science/pith/IJ3SDNCIFZB6IUPQFCOMTQZPI6/bundle.json","state":"https://pith.science/pith/IJ3SDNCIFZB6IUPQFCOMTQZPI6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IJ3SDNCIFZB6IUPQFCOMTQZPI6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:IJ3SDNCIFZB6IUPQFCOMTQZPI6","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":"b4df8991be0350f10233f3a71abb1de2ab5e68c7815ecdc4a9819fc7cc53b411","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-04-03T06:32:04Z","title_canon_sha256":"ce1455d06c4ebb6d7041083bf63e711413a2c84af2fdc66ca94a55d9269e334b"},"schema_version":"1.0","source":{"id":"1204.0605","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.0605","created_at":"2026-05-18T03:58:39Z"},{"alias_kind":"arxiv_version","alias_value":"1204.0605v1","created_at":"2026-05-18T03:58:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.0605","created_at":"2026-05-18T03:58:39Z"},{"alias_kind":"pith_short_12","alias_value":"IJ3SDNCIFZB6","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IJ3SDNCIFZB6IUPQ","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IJ3SDNCI","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:0469d8f19533ca72808b8817d42aadc4893634aea6b41547c503bf2ac35e36d8","target":"graph","created_at":"2026-05-18T03:58:39Z","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":"The aim of our paper is to prove the Triple Representation Theorem, which was established by Jen\\v{c}a in the setting of complete lattice effect algebras, for a special class of homogeneous effect algebras, namely TRT-effect algebras. This class includes complete lattice effect algebras, sharply dominating Archimedean atomic lattice effect algebras and homogeneous orthocomplete effect algebras.","authors_text":"Jan Paseka, Josef Niederle","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-04-03T06:32:04Z","title":"Triple Representation Theorem for homogeneous effect algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.0605","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:ad0abe42e0897ce52336a33efdf14c880a0c74e0682536430a0643cebafeccea","target":"record","created_at":"2026-05-18T03:58:39Z","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":"b4df8991be0350f10233f3a71abb1de2ab5e68c7815ecdc4a9819fc7cc53b411","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-04-03T06:32:04Z","title_canon_sha256":"ce1455d06c4ebb6d7041083bf63e711413a2c84af2fdc66ca94a55d9269e334b"},"schema_version":"1.0","source":{"id":"1204.0605","kind":"arxiv","version":1}},"canonical_sha256":"427721b4482e43e451f0289cc9c32f479522f7fa00a80e98a52194220cb82e74","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"427721b4482e43e451f0289cc9c32f479522f7fa00a80e98a52194220cb82e74","first_computed_at":"2026-05-18T03:58:39.026670Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:58:39.026670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P0W9JgkeycKskktTtbtrjPCboRThsbk5kxpUgH+5Qo51tPyDNCPzwW0OWcIw0nXwlLQZDs6+EID5bBClK5diBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:58:39.027258Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.0605","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad0abe42e0897ce52336a33efdf14c880a0c74e0682536430a0643cebafeccea","sha256:0469d8f19533ca72808b8817d42aadc4893634aea6b41547c503bf2ac35e36d8"],"state_sha256":"a6999e849c0ffa71d9552c1ae894675d0f4e884559f6f2802593294e46c74b12"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HQKzafZWZPfek7vmLhQIzlSzDSFHvWLU1vTZwMAO21R6x3gW1XTvQ1mw1JD5zy92GWXNUdabxJyXkhU4Yqr9DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T11:44:28.487548Z","bundle_sha256":"11ddd73dbda5eef8d6e97595892e097587dca4eaed6597bad39324f9ba73ddd0"}}