{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:PNGPS7OTK4NI2QWLELOZPG4X3U","short_pith_number":"pith:PNGPS7OT","canonical_record":{"source":{"id":"1202.2033","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-02-09T16:17:14Z","cross_cats_sorted":["math.FA","math.MP"],"title_canon_sha256":"2993a84d5e71dc747809cfa7ac1f4f8dbcbad6672dc9d761b10de4886bc62057","abstract_canon_sha256":"0bd9baaabbfb7ef9b6c89c4e4bd2695304914a743831995ab3f1c47658f884e8"},"schema_version":"1.0"},"canonical_sha256":"7b4cf97dd3571a8d42cb22dd979b97dd01931f3ede981833a4a9ac9ccc630a50","source":{"kind":"arxiv","id":"1202.2033","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2033","created_at":"2026-05-18T01:28:35Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2033v2","created_at":"2026-05-18T01:28:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2033","created_at":"2026-05-18T01:28:35Z"},{"alias_kind":"pith_short_12","alias_value":"PNGPS7OTK4NI","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PNGPS7OTK4NI2QWL","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PNGPS7OT","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:PNGPS7OTK4NI2QWLELOZPG4X3U","target":"record","payload":{"canonical_record":{"source":{"id":"1202.2033","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-02-09T16:17:14Z","cross_cats_sorted":["math.FA","math.MP"],"title_canon_sha256":"2993a84d5e71dc747809cfa7ac1f4f8dbcbad6672dc9d761b10de4886bc62057","abstract_canon_sha256":"0bd9baaabbfb7ef9b6c89c4e4bd2695304914a743831995ab3f1c47658f884e8"},"schema_version":"1.0"},"canonical_sha256":"7b4cf97dd3571a8d42cb22dd979b97dd01931f3ede981833a4a9ac9ccc630a50","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:35.699938Z","signature_b64":"edGQ9F6ngoS7cTs7f/nbenmGzxjAqwdcjBX1dGYUU7UEGl9Kp0oI/yA/iqgwbLQydVA8p2ceh8D5Xa9jXXFoCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7b4cf97dd3571a8d42cb22dd979b97dd01931f3ede981833a4a9ac9ccc630a50","last_reissued_at":"2026-05-18T01:28:35.699446Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:35.699446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.2033","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":"2026-05-18T01:28:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qyuXvj8XBIFd+1SNZdE+lNtxr79RoH4juty6r4JS2QN6vgVFwHttRjIG5pLNpkNI7DfMmwA6d3IZ66Wn7CkNDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T03:04:38.753774Z"},"content_sha256":"88127c685638d90d60d115505a07f33eec155004cd1e636ffcbc3367bc56eb4e","schema_version":"1.0","event_id":"sha256:88127c685638d90d60d115505a07f33eec155004cd1e636ffcbc3367bc56eb4e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:PNGPS7OTK4NI2QWLELOZPG4X3U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Discrete-Time Path Distributions on Hilbert Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.MP"],"primary_cat":"math-ph","authors_text":"Mathieu Beau (STP-DIAS), T. C. Dorlas (STP-DIAS)","submitted_at":"2012-02-09T16:17:14Z","abstract_excerpt":"We construct a path distribution representing the kinetic part of the Feynman path integral at discrete times similar to that defined by Thomas [1], but on a Hilbert space of paths rather than a nuclear sequence space. We also consider different boundary conditions and show that the discrete-time Feynman path integral is well-defined for suitably smooth potentials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2033","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":""},"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":"2026-05-18T01:28:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0pTrMGyPtp2ptWDEZHdmcnL9yn8Dc9TfFKbBEwu9N9irtLs/WQgp6wBzNSlBpRiIX+9pa9/b3nIyyKng+hoBBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T03:04:38.754402Z"},"content_sha256":"cc04e0cc8794070083130abf507f6a058a521f02424b0632b3604e9bde147ece","schema_version":"1.0","event_id":"sha256:cc04e0cc8794070083130abf507f6a058a521f02424b0632b3604e9bde147ece"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PNGPS7OTK4NI2QWLELOZPG4X3U/bundle.json","state_url":"https://pith.science/pith/PNGPS7OTK4NI2QWLELOZPG4X3U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PNGPS7OTK4NI2QWLELOZPG4X3U/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":"2026-06-24T03:04:38Z","links":{"resolver":"https://pith.science/pith/PNGPS7OTK4NI2QWLELOZPG4X3U","bundle":"https://pith.science/pith/PNGPS7OTK4NI2QWLELOZPG4X3U/bundle.json","state":"https://pith.science/pith/PNGPS7OTK4NI2QWLELOZPG4X3U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PNGPS7OTK4NI2QWLELOZPG4X3U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:PNGPS7OTK4NI2QWLELOZPG4X3U","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":"0bd9baaabbfb7ef9b6c89c4e4bd2695304914a743831995ab3f1c47658f884e8","cross_cats_sorted":["math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-02-09T16:17:14Z","title_canon_sha256":"2993a84d5e71dc747809cfa7ac1f4f8dbcbad6672dc9d761b10de4886bc62057"},"schema_version":"1.0","source":{"id":"1202.2033","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2033","created_at":"2026-05-18T01:28:35Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2033v2","created_at":"2026-05-18T01:28:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2033","created_at":"2026-05-18T01:28:35Z"},{"alias_kind":"pith_short_12","alias_value":"PNGPS7OTK4NI","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PNGPS7OTK4NI2QWL","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PNGPS7OT","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:cc04e0cc8794070083130abf507f6a058a521f02424b0632b3604e9bde147ece","target":"graph","created_at":"2026-05-18T01:28:35Z","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 construct a path distribution representing the kinetic part of the Feynman path integral at discrete times similar to that defined by Thomas [1], but on a Hilbert space of paths rather than a nuclear sequence space. We also consider different boundary conditions and show that the discrete-time Feynman path integral is well-defined for suitably smooth potentials.","authors_text":"Mathieu Beau (STP-DIAS), T. C. Dorlas (STP-DIAS)","cross_cats":["math.FA","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-02-09T16:17:14Z","title":"Discrete-Time Path Distributions on Hilbert Space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2033","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":"sha256:88127c685638d90d60d115505a07f33eec155004cd1e636ffcbc3367bc56eb4e","target":"record","created_at":"2026-05-18T01:28:35Z","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":"0bd9baaabbfb7ef9b6c89c4e4bd2695304914a743831995ab3f1c47658f884e8","cross_cats_sorted":["math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-02-09T16:17:14Z","title_canon_sha256":"2993a84d5e71dc747809cfa7ac1f4f8dbcbad6672dc9d761b10de4886bc62057"},"schema_version":"1.0","source":{"id":"1202.2033","kind":"arxiv","version":2}},"canonical_sha256":"7b4cf97dd3571a8d42cb22dd979b97dd01931f3ede981833a4a9ac9ccc630a50","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7b4cf97dd3571a8d42cb22dd979b97dd01931f3ede981833a4a9ac9ccc630a50","first_computed_at":"2026-05-18T01:28:35.699446Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:35.699446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"edGQ9F6ngoS7cTs7f/nbenmGzxjAqwdcjBX1dGYUU7UEGl9Kp0oI/yA/iqgwbLQydVA8p2ceh8D5Xa9jXXFoCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:35.699938Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.2033","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88127c685638d90d60d115505a07f33eec155004cd1e636ffcbc3367bc56eb4e","sha256:cc04e0cc8794070083130abf507f6a058a521f02424b0632b3604e9bde147ece"],"state_sha256":"15d19f66bb2d446d862ca10787f9f5dbef94af017cdd21c59e46c1dfa117bfc6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TA3YZIwYwvzcwTArXoED6GAkkAFDboXZ0iAJOrdeJaT7ktCByBIbGJ9HYL0O/i/bZp0AGVdNLEZfNddqCzvwBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T03:04:38.757991Z","bundle_sha256":"514262db8453b40f31977792265dac886ee50a11d57c492e039cebb152ba5d66"}}