{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:5R2L6AT2N3GTGTEXY77RXQ6A22","short_pith_number":"pith:5R2L6AT2","canonical_record":{"source":{"id":"quant-ph/0604178","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2006-04-24T14:37:43Z","cross_cats_sorted":[],"title_canon_sha256":"76894e3a9f94a61ad5dcac9b3af70e0856cc45317aa983e14d20ee429aaf161f","abstract_canon_sha256":"2c0a382f86ace5e1c122fb64976c5cc7ef6a338496ff95ca29b3bd2cfc017249"},"schema_version":"1.0"},"canonical_sha256":"ec74bf027a6ecd334c97c7ff1bc3c0d683469d3ebbe9487f5be7d760db5d558a","source":{"kind":"arxiv","id":"quant-ph/0604178","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0604178","created_at":"2026-07-04T17:02:59Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0604178v1","created_at":"2026-07-04T17:02:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0604178","created_at":"2026-07-04T17:02:59Z"},{"alias_kind":"pith_short_12","alias_value":"5R2L6AT2N3GT","created_at":"2026-07-04T17:02:59Z"},{"alias_kind":"pith_short_16","alias_value":"5R2L6AT2N3GTGTEX","created_at":"2026-07-04T17:02:59Z"},{"alias_kind":"pith_short_8","alias_value":"5R2L6AT2","created_at":"2026-07-04T17:02:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:5R2L6AT2N3GTGTEXY77RXQ6A22","target":"record","payload":{"canonical_record":{"source":{"id":"quant-ph/0604178","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2006-04-24T14:37:43Z","cross_cats_sorted":[],"title_canon_sha256":"76894e3a9f94a61ad5dcac9b3af70e0856cc45317aa983e14d20ee429aaf161f","abstract_canon_sha256":"2c0a382f86ace5e1c122fb64976c5cc7ef6a338496ff95ca29b3bd2cfc017249"},"schema_version":"1.0"},"canonical_sha256":"ec74bf027a6ecd334c97c7ff1bc3c0d683469d3ebbe9487f5be7d760db5d558a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T17:02:59.858522Z","signature_b64":"kAExY6UXsKEmLsZglhU9KiJsmWxbaPEKMzAWf6FZwagL3wyO8IjE1HlrNSinYVaJy7202mvlZjx15ai2Vd1rDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec74bf027a6ecd334c97c7ff1bc3c0d683469d3ebbe9487f5be7d760db5d558a","last_reissued_at":"2026-07-04T17:02:59.858175Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T17:02:59.858175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"quant-ph/0604178","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":"2026-07-04T17:02:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q6kaErWQlrBywRCHNJP/lmDhe4ZO34QI8zAIKZGLzDdQAGyiQTlo7NNJqJrbPKhG+62fH9xI4hOnjs4s14MQCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T00:27:06.108155Z"},"content_sha256":"90d51cadd0372e174c87f05a5b1ae1add293575ffe600f082a7ff183ad314d69","schema_version":"1.0","event_id":"sha256:90d51cadd0372e174c87f05a5b1ae1add293575ffe600f082a7ff183ad314d69"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:5R2L6AT2N3GTGTEXY77RXQ6A22","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Born Rule in Quantum and Classical Mechanics","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Jiangbin Gong, Paul Brumer","submitted_at":"2006-04-24T14:37:43Z","abstract_excerpt":"Considerable effort has been devoted to deriving the Born rule (e.g. that $|\\psi(x)|^2 dx$ is the probability of finding a system, described by $\\psi$, between $x$ and $x + dx$) in quantum mechanics. Here we show that the Born rule is not solely quantum mechanical; rather, it arises naturally in the Hilbert space formulation of {\\it classical} mechanics as well. These results provide new insights into the nature of the Born rule, and impact on its understanding in the framework of quantum mechanics."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0604178","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/quant-ph/0604178/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":"2026-07-04T17:02:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"faF5iLcwsksxAYtK/e0aIuDWvXo9Eda0qv1gfBpENpycOk7iR2M+beF6NBpQAUxusNuQOX4vldzx6YllYXzyAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T00:27:06.108517Z"},"content_sha256":"63d75b7af6f82afeb3200143e48282bc2c5529181241934df28963dce3a65e46","schema_version":"1.0","event_id":"sha256:63d75b7af6f82afeb3200143e48282bc2c5529181241934df28963dce3a65e46"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5R2L6AT2N3GTGTEXY77RXQ6A22/bundle.json","state_url":"https://pith.science/pith/5R2L6AT2N3GTGTEXY77RXQ6A22/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5R2L6AT2N3GTGTEXY77RXQ6A22/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":"2026-07-05T00:27:06Z","links":{"resolver":"https://pith.science/pith/5R2L6AT2N3GTGTEXY77RXQ6A22","bundle":"https://pith.science/pith/5R2L6AT2N3GTGTEXY77RXQ6A22/bundle.json","state":"https://pith.science/pith/5R2L6AT2N3GTGTEXY77RXQ6A22/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5R2L6AT2N3GTGTEXY77RXQ6A22/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:5R2L6AT2N3GTGTEXY77RXQ6A22","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":"2c0a382f86ace5e1c122fb64976c5cc7ef6a338496ff95ca29b3bd2cfc017249","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2006-04-24T14:37:43Z","title_canon_sha256":"76894e3a9f94a61ad5dcac9b3af70e0856cc45317aa983e14d20ee429aaf161f"},"schema_version":"1.0","source":{"id":"quant-ph/0604178","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0604178","created_at":"2026-07-04T17:02:59Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0604178v1","created_at":"2026-07-04T17:02:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0604178","created_at":"2026-07-04T17:02:59Z"},{"alias_kind":"pith_short_12","alias_value":"5R2L6AT2N3GT","created_at":"2026-07-04T17:02:59Z"},{"alias_kind":"pith_short_16","alias_value":"5R2L6AT2N3GTGTEX","created_at":"2026-07-04T17:02:59Z"},{"alias_kind":"pith_short_8","alias_value":"5R2L6AT2","created_at":"2026-07-04T17:02:59Z"}],"graph_snapshots":[{"event_id":"sha256:63d75b7af6f82afeb3200143e48282bc2c5529181241934df28963dce3a65e46","target":"graph","created_at":"2026-07-04T17:02:59Z","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/quant-ph/0604178/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Considerable effort has been devoted to deriving the Born rule (e.g. that $|\\psi(x)|^2 dx$ is the probability of finding a system, described by $\\psi$, between $x$ and $x + dx$) in quantum mechanics. Here we show that the Born rule is not solely quantum mechanical; rather, it arises naturally in the Hilbert space formulation of {\\it classical} mechanics as well. These results provide new insights into the nature of the Born rule, and impact on its understanding in the framework of quantum mechanics.","authors_text":"Jiangbin Gong, Paul Brumer","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2006-04-24T14:37:43Z","title":"The Born Rule in Quantum and Classical Mechanics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0604178","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":"sha256:90d51cadd0372e174c87f05a5b1ae1add293575ffe600f082a7ff183ad314d69","target":"record","created_at":"2026-07-04T17:02:59Z","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":"2c0a382f86ace5e1c122fb64976c5cc7ef6a338496ff95ca29b3bd2cfc017249","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2006-04-24T14:37:43Z","title_canon_sha256":"76894e3a9f94a61ad5dcac9b3af70e0856cc45317aa983e14d20ee429aaf161f"},"schema_version":"1.0","source":{"id":"quant-ph/0604178","kind":"arxiv","version":1}},"canonical_sha256":"ec74bf027a6ecd334c97c7ff1bc3c0d683469d3ebbe9487f5be7d760db5d558a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec74bf027a6ecd334c97c7ff1bc3c0d683469d3ebbe9487f5be7d760db5d558a","first_computed_at":"2026-07-04T17:02:59.858175Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T17:02:59.858175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kAExY6UXsKEmLsZglhU9KiJsmWxbaPEKMzAWf6FZwagL3wyO8IjE1HlrNSinYVaJy7202mvlZjx15ai2Vd1rDw==","signature_status":"signed_v1","signed_at":"2026-07-04T17:02:59.858522Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0604178","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90d51cadd0372e174c87f05a5b1ae1add293575ffe600f082a7ff183ad314d69","sha256:63d75b7af6f82afeb3200143e48282bc2c5529181241934df28963dce3a65e46"],"state_sha256":"8505196b0e4b88aed98bc802d1ef187fd5f4b5711b2984f6acd3d57613c2ec2f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vcsRb6qqG4JqOxo3pwIVBIH6NsQZKaXx8cfOsjfalm+fEKpKp5CMiGZw8TWhWX8InqWxN2T80wkNqTDd0RoTDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T00:27:06.110251Z","bundle_sha256":"72a62c37cab1aad0c2efc66068a7d43552c01a0f575167fd958b8263643aaff6"}}