{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:IBIHZXVFHVUWLCTLCNSL562FVT","short_pith_number":"pith:IBIHZXVF","canonical_record":{"source":{"id":"2606.08902","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2026-06-08T01:05:09Z","cross_cats_sorted":["econ.TH"],"title_canon_sha256":"11a136ea12e1f7c87cb645427b61fe572043a3e4bbde13d03db94869e57b007a","abstract_canon_sha256":"b74822b5cf4b24d5aebe0a2d2fc6a9f0e98ba8cd584bc22373e1dfc1b2035a9a"},"schema_version":"1.0"},"canonical_sha256":"40507cdea53d69658a6b1364befb45acc3d4f0184fa7a31dc73963b1fa97f038","source":{"kind":"arxiv","id":"2606.08902","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.08902","created_at":"2026-06-09T02:07:46Z"},{"alias_kind":"arxiv_version","alias_value":"2606.08902v1","created_at":"2026-06-09T02:07:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.08902","created_at":"2026-06-09T02:07:46Z"},{"alias_kind":"pith_short_12","alias_value":"IBIHZXVFHVUW","created_at":"2026-06-09T02:07:46Z"},{"alias_kind":"pith_short_16","alias_value":"IBIHZXVFHVUWLCTL","created_at":"2026-06-09T02:07:46Z"},{"alias_kind":"pith_short_8","alias_value":"IBIHZXVF","created_at":"2026-06-09T02:07:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:IBIHZXVFHVUWLCTLCNSL562FVT","target":"record","payload":{"canonical_record":{"source":{"id":"2606.08902","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2026-06-08T01:05:09Z","cross_cats_sorted":["econ.TH"],"title_canon_sha256":"11a136ea12e1f7c87cb645427b61fe572043a3e4bbde13d03db94869e57b007a","abstract_canon_sha256":"b74822b5cf4b24d5aebe0a2d2fc6a9f0e98ba8cd584bc22373e1dfc1b2035a9a"},"schema_version":"1.0"},"canonical_sha256":"40507cdea53d69658a6b1364befb45acc3d4f0184fa7a31dc73963b1fa97f038","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T02:07:46.333756Z","signature_b64":"mwmAw6A8kHi+nG/gFgZOW9DgYMQMdV2UbNOF/U/UQV3tvDtRBj1uUaNmNagnY3suIzsE6KKcCzRi+tW0uvCiAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"40507cdea53d69658a6b1364befb45acc3d4f0184fa7a31dc73963b1fa97f038","last_reissued_at":"2026-06-09T02:07:46.332897Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T02:07:46.332897Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.08902","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":"2026-06-09T02:07:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aPgiLAnn+gdBj63qTN7gwpalH/KeGtiil/e+BbVQkOJQL86e5XZCR3HdXzud8TjLipL3O2aJ+mT7UE0j0u7mBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-19T21:25:17.700643Z"},"content_sha256":"1efad1cd59a8c56488389b2c5b32a07a24100b33e4cfa7fdcd1a1e438d71cdbb","schema_version":"1.0","event_id":"sha256:1efad1cd59a8c56488389b2c5b32a07a24100b33e4cfa7fdcd1a1e438d71cdbb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:IBIHZXVFHVUWLCTLCNSL562FVT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Kernel-Clean Lean Mechanization of Classical Lottery in Action and the Wakker--Debreu--Koopmans Representation Layer","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["econ.TH"],"primary_cat":"cs.LO","authors_text":"Fan Wang, Ilia Tsetlin, Jingyuan Li","submitted_at":"2026-06-08T01:05:09Z","abstract_excerpt":"We present a Lean 4/Mathlib formalization of the additive representation theory behind Classical Lottery in Action and the Wakker-Debreu-Koopmans (WDK) layer it relies on. Our central result is a machine-checked proof that the cross-pair Thomsen / double-cancellation (hexagon) condition is irreducible from the ordinal axioms of additive conjoint measurement (weak order, restricted solvability, Archimedean condition, and tradeoff consistency). We exhibit an explicit verified counter-model (additiveRealBoolPref) satisfying all ordinal axioms yet failing the cross-pair condition, with every stric"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08902","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.08902/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-09T02:07:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Szcyj+k+J3aqbfSwm0NqclqCcfSi1M20xDKgNVmxvu31ygjPa2FWq6czsWrdOow1f7zsqwzlBMM4jo82CRmzBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-19T21:25:17.701025Z"},"content_sha256":"31378c90a24c30cbba502b70cd50d22bb9f6ab16a84bd22b27ccaaf8049b9ba0","schema_version":"1.0","event_id":"sha256:31378c90a24c30cbba502b70cd50d22bb9f6ab16a84bd22b27ccaaf8049b9ba0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IBIHZXVFHVUWLCTLCNSL562FVT/bundle.json","state_url":"https://pith.science/pith/IBIHZXVFHVUWLCTLCNSL562FVT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IBIHZXVFHVUWLCTLCNSL562FVT/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":"2026-06-19T21:25:17Z","links":{"resolver":"https://pith.science/pith/IBIHZXVFHVUWLCTLCNSL562FVT","bundle":"https://pith.science/pith/IBIHZXVFHVUWLCTLCNSL562FVT/bundle.json","state":"https://pith.science/pith/IBIHZXVFHVUWLCTLCNSL562FVT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IBIHZXVFHVUWLCTLCNSL562FVT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:IBIHZXVFHVUWLCTLCNSL562FVT","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":"b74822b5cf4b24d5aebe0a2d2fc6a9f0e98ba8cd584bc22373e1dfc1b2035a9a","cross_cats_sorted":["econ.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2026-06-08T01:05:09Z","title_canon_sha256":"11a136ea12e1f7c87cb645427b61fe572043a3e4bbde13d03db94869e57b007a"},"schema_version":"1.0","source":{"id":"2606.08902","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.08902","created_at":"2026-06-09T02:07:46Z"},{"alias_kind":"arxiv_version","alias_value":"2606.08902v1","created_at":"2026-06-09T02:07:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.08902","created_at":"2026-06-09T02:07:46Z"},{"alias_kind":"pith_short_12","alias_value":"IBIHZXVFHVUW","created_at":"2026-06-09T02:07:46Z"},{"alias_kind":"pith_short_16","alias_value":"IBIHZXVFHVUWLCTL","created_at":"2026-06-09T02:07:46Z"},{"alias_kind":"pith_short_8","alias_value":"IBIHZXVF","created_at":"2026-06-09T02:07:46Z"}],"graph_snapshots":[{"event_id":"sha256:31378c90a24c30cbba502b70cd50d22bb9f6ab16a84bd22b27ccaaf8049b9ba0","target":"graph","created_at":"2026-06-09T02:07:46Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.08902/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a Lean 4/Mathlib formalization of the additive representation theory behind Classical Lottery in Action and the Wakker-Debreu-Koopmans (WDK) layer it relies on. Our central result is a machine-checked proof that the cross-pair Thomsen / double-cancellation (hexagon) condition is irreducible from the ordinal axioms of additive conjoint measurement (weak order, restricted solvability, Archimedean condition, and tradeoff consistency). We exhibit an explicit verified counter-model (additiveRealBoolPref) satisfying all ordinal axioms yet failing the cross-pair condition, with every stric","authors_text":"Fan Wang, Ilia Tsetlin, Jingyuan Li","cross_cats":["econ.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2026-06-08T01:05:09Z","title":"A Kernel-Clean Lean Mechanization of Classical Lottery in Action and the Wakker--Debreu--Koopmans Representation Layer"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08902","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":"sha256:1efad1cd59a8c56488389b2c5b32a07a24100b33e4cfa7fdcd1a1e438d71cdbb","target":"record","created_at":"2026-06-09T02:07:46Z","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":"b74822b5cf4b24d5aebe0a2d2fc6a9f0e98ba8cd584bc22373e1dfc1b2035a9a","cross_cats_sorted":["econ.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2026-06-08T01:05:09Z","title_canon_sha256":"11a136ea12e1f7c87cb645427b61fe572043a3e4bbde13d03db94869e57b007a"},"schema_version":"1.0","source":{"id":"2606.08902","kind":"arxiv","version":1}},"canonical_sha256":"40507cdea53d69658a6b1364befb45acc3d4f0184fa7a31dc73963b1fa97f038","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"40507cdea53d69658a6b1364befb45acc3d4f0184fa7a31dc73963b1fa97f038","first_computed_at":"2026-06-09T02:07:46.332897Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T02:07:46.332897Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mwmAw6A8kHi+nG/gFgZOW9DgYMQMdV2UbNOF/U/UQV3tvDtRBj1uUaNmNagnY3suIzsE6KKcCzRi+tW0uvCiAw==","signature_status":"signed_v1","signed_at":"2026-06-09T02:07:46.333756Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.08902","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1efad1cd59a8c56488389b2c5b32a07a24100b33e4cfa7fdcd1a1e438d71cdbb","sha256:31378c90a24c30cbba502b70cd50d22bb9f6ab16a84bd22b27ccaaf8049b9ba0"],"state_sha256":"678636f466c81d047d5ec4fea4c7cbbd0a8ead137530ffd47b81e5a505b9b86e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QfVgwUxAYp5yVoZZqty5UVeJ9BSJyQ+2+kddmjFAT0V5A/T9DD9ejAYpSSfw9Qoh7oC6ZCpQhlf0mMHYwn3VBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-19T21:25:17.703085Z","bundle_sha256":"4f84f143ca07f722cbab281beb12bf7c6a5bfe192fc93a9330dbc83f9a9f870c"}}