{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:F72QAJIQVRVEHJKW3EY7DV3GEN","short_pith_number":"pith:F72QAJIQ","canonical_record":{"source":{"id":"2507.04812","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2025-07-07T09:31:32Z","cross_cats_sorted":["math-ph","math.MP","physics.hist-ph"],"title_canon_sha256":"31b2bc2c14affd6ea0d2b3fc9f3986459948ceffca9a462781da642097d845cc","abstract_canon_sha256":"b89291b7891b4a301bfce40e0ac62d85b69515ffc20dc34b12453c829909c936"},"schema_version":"1.0"},"canonical_sha256":"2ff5002510ac6a43a556d931f1d7662379242c92577b3d1e4eb1d1daeb3434b0","source":{"kind":"arxiv","id":"2507.04812","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.04812","created_at":"2026-07-05T11:33:26Z"},{"alias_kind":"arxiv_version","alias_value":"2507.04812v2","created_at":"2026-07-05T11:33:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.04812","created_at":"2026-07-05T11:33:26Z"},{"alias_kind":"pith_short_12","alias_value":"F72QAJIQVRVE","created_at":"2026-07-05T11:33:26Z"},{"alias_kind":"pith_short_16","alias_value":"F72QAJIQVRVEHJKW","created_at":"2026-07-05T11:33:26Z"},{"alias_kind":"pith_short_8","alias_value":"F72QAJIQ","created_at":"2026-07-05T11:33:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:F72QAJIQVRVEHJKW3EY7DV3GEN","target":"record","payload":{"canonical_record":{"source":{"id":"2507.04812","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2025-07-07T09:31:32Z","cross_cats_sorted":["math-ph","math.MP","physics.hist-ph"],"title_canon_sha256":"31b2bc2c14affd6ea0d2b3fc9f3986459948ceffca9a462781da642097d845cc","abstract_canon_sha256":"b89291b7891b4a301bfce40e0ac62d85b69515ffc20dc34b12453c829909c936"},"schema_version":"1.0"},"canonical_sha256":"2ff5002510ac6a43a556d931f1d7662379242c92577b3d1e4eb1d1daeb3434b0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:33:26.868694Z","signature_b64":"Teo2VO486vZZWiNQsWKxprRlc5rKmxzjjovskhrH4tXI/MMsgTh6kbaFQtBfqi2OyNq+ZtSpEAv8dOzo/C4nAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ff5002510ac6a43a556d931f1d7662379242c92577b3d1e4eb1d1daeb3434b0","last_reissued_at":"2026-07-05T11:33:26.868211Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:33:26.868211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.04812","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:33:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4mxyaQN3nJRCQ2iyqI5WeU53DAx2hrHpniv//4hprB/E6BrlygBu99SVw5/sAjv36Ebxn6In280EDFfXtxFrCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T09:22:38.065925Z"},"content_sha256":"2ee66a95b628b5c514ead86d6af37e25a768f729d11cfa9e4da613d2f38f9ca3","schema_version":"1.0","event_id":"sha256:2ee66a95b628b5c514ead86d6af37e25a768f729d11cfa9e4da613d2f38f9ca3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:F72QAJIQVRVEHJKW3EY7DV3GEN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Phenomenological quantum mechanics II: deducing the formalism from experimental observations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP","physics.hist-ph"],"primary_cat":"quant-ph","authors_text":"Dariusz Chru\\'sci\\'nski, Davide Lonigro, Fattah Sakuldee, {\\L}ukasz Cywi\\'nski, Piotr Sza\\'nkowski","submitted_at":"2025-07-07T09:31:32Z","abstract_excerpt":"We propose an exercise in which one attempts to deduce the formalism of quantum mechanics solely from phenomenological observations. The only assumed inputs are the multi-time probability distributions estimated from the results of sequential measurements of quantum observables; no presuppositions about the underlying mathematical structures are permitted. In the concluding Part II of the paper, we carry out the deduction of the formalism from the phenomenological inputs described in Part I. We show that the resulting formalism exhibits an affinity with Hilbert spaces, and we derive an explici"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.04812","kind":"arxiv","version":2},"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/2507.04812/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":"2026-07-05T11:33:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P5AurjiqZ3sobuenlVQ1bmw/iC4ekTeFVjnajHE5H8R7zukqBsPbjvoHYmt2lLQml27S8sSU65GLfIuHDm2cDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T09:22:38.066863Z"},"content_sha256":"344c78814ae75b741df6167513c117230b8796acd2058ee322c70222c4b7e35c","schema_version":"1.0","event_id":"sha256:344c78814ae75b741df6167513c117230b8796acd2058ee322c70222c4b7e35c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F72QAJIQVRVEHJKW3EY7DV3GEN/bundle.json","state_url":"https://pith.science/pith/F72QAJIQVRVEHJKW3EY7DV3GEN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F72QAJIQVRVEHJKW3EY7DV3GEN/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":"2026-08-13T09:22:38Z","links":{"resolver":"https://pith.science/pith/F72QAJIQVRVEHJKW3EY7DV3GEN","bundle":"https://pith.science/pith/F72QAJIQVRVEHJKW3EY7DV3GEN/bundle.json","state":"https://pith.science/pith/F72QAJIQVRVEHJKW3EY7DV3GEN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F72QAJIQVRVEHJKW3EY7DV3GEN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:F72QAJIQVRVEHJKW3EY7DV3GEN","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":"b89291b7891b4a301bfce40e0ac62d85b69515ffc20dc34b12453c829909c936","cross_cats_sorted":["math-ph","math.MP","physics.hist-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2025-07-07T09:31:32Z","title_canon_sha256":"31b2bc2c14affd6ea0d2b3fc9f3986459948ceffca9a462781da642097d845cc"},"schema_version":"1.0","source":{"id":"2507.04812","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.04812","created_at":"2026-07-05T11:33:26Z"},{"alias_kind":"arxiv_version","alias_value":"2507.04812v2","created_at":"2026-07-05T11:33:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.04812","created_at":"2026-07-05T11:33:26Z"},{"alias_kind":"pith_short_12","alias_value":"F72QAJIQVRVE","created_at":"2026-07-05T11:33:26Z"},{"alias_kind":"pith_short_16","alias_value":"F72QAJIQVRVEHJKW","created_at":"2026-07-05T11:33:26Z"},{"alias_kind":"pith_short_8","alias_value":"F72QAJIQ","created_at":"2026-07-05T11:33:26Z"}],"graph_snapshots":[{"event_id":"sha256:344c78814ae75b741df6167513c117230b8796acd2058ee322c70222c4b7e35c","target":"graph","created_at":"2026-07-05T11:33:26Z","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/2507.04812/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose an exercise in which one attempts to deduce the formalism of quantum mechanics solely from phenomenological observations. The only assumed inputs are the multi-time probability distributions estimated from the results of sequential measurements of quantum observables; no presuppositions about the underlying mathematical structures are permitted. In the concluding Part II of the paper, we carry out the deduction of the formalism from the phenomenological inputs described in Part I. We show that the resulting formalism exhibits an affinity with Hilbert spaces, and we derive an explici","authors_text":"Dariusz Chru\\'sci\\'nski, Davide Lonigro, Fattah Sakuldee, {\\L}ukasz Cywi\\'nski, Piotr Sza\\'nkowski","cross_cats":["math-ph","math.MP","physics.hist-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2025-07-07T09:31:32Z","title":"Phenomenological quantum mechanics II: deducing the formalism from experimental observations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.04812","kind":"arxiv","version":2},"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":"sha256:2ee66a95b628b5c514ead86d6af37e25a768f729d11cfa9e4da613d2f38f9ca3","target":"record","created_at":"2026-07-05T11:33:26Z","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":"b89291b7891b4a301bfce40e0ac62d85b69515ffc20dc34b12453c829909c936","cross_cats_sorted":["math-ph","math.MP","physics.hist-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2025-07-07T09:31:32Z","title_canon_sha256":"31b2bc2c14affd6ea0d2b3fc9f3986459948ceffca9a462781da642097d845cc"},"schema_version":"1.0","source":{"id":"2507.04812","kind":"arxiv","version":2}},"canonical_sha256":"2ff5002510ac6a43a556d931f1d7662379242c92577b3d1e4eb1d1daeb3434b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ff5002510ac6a43a556d931f1d7662379242c92577b3d1e4eb1d1daeb3434b0","first_computed_at":"2026-07-05T11:33:26.868211Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:33:26.868211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Teo2VO486vZZWiNQsWKxprRlc5rKmxzjjovskhrH4tXI/MMsgTh6kbaFQtBfqi2OyNq+ZtSpEAv8dOzo/C4nAA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:33:26.868694Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.04812","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ee66a95b628b5c514ead86d6af37e25a768f729d11cfa9e4da613d2f38f9ca3","sha256:344c78814ae75b741df6167513c117230b8796acd2058ee322c70222c4b7e35c"],"state_sha256":"9ae4b5bf75d834af704352e35ca6f8555242345fd30736e29237ecb85b967513"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s+dDXERUp/TWF8yMYjCQrxMsAw6VMDmADloW35lkSUNCQ1CNW7CU4YWP2E1LhbZ6yApsSAv1OPJ6cQ4x+ydTCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T09:22:38.073609Z","bundle_sha256":"12c3825cf0a6cd45c0c4c4a7c8074e7ad646350dc6fb7b2d9473b545a5a55dc4"}}