{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:WWFJSUN6VBGT56SOAPJ6CJYZRM","short_pith_number":"pith:WWFJSUN6","canonical_record":{"source":{"id":"1804.00834","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-04-03T06:00:48Z","cross_cats_sorted":[],"title_canon_sha256":"10a68e891314855b04b782685ceef9679938f22f8f35fefa8f9ef92cdeb32a67","abstract_canon_sha256":"b9986321bbfc0187243ff028119e2bfa9a53a82745adc57eebf91916119bdfd1"},"schema_version":"1.0"},"canonical_sha256":"b58a9951bea84d3efa4e03d3e127198b1c71d633521d624e653d5758465badbd","source":{"kind":"arxiv","id":"1804.00834","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.00834","created_at":"2026-05-18T00:06:40Z"},{"alias_kind":"arxiv_version","alias_value":"1804.00834v2","created_at":"2026-05-18T00:06:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.00834","created_at":"2026-05-18T00:06:40Z"},{"alias_kind":"pith_short_12","alias_value":"WWFJSUN6VBGT","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"WWFJSUN6VBGT56SO","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"WWFJSUN6","created_at":"2026-05-18T12:33:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:WWFJSUN6VBGT56SOAPJ6CJYZRM","target":"record","payload":{"canonical_record":{"source":{"id":"1804.00834","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-04-03T06:00:48Z","cross_cats_sorted":[],"title_canon_sha256":"10a68e891314855b04b782685ceef9679938f22f8f35fefa8f9ef92cdeb32a67","abstract_canon_sha256":"b9986321bbfc0187243ff028119e2bfa9a53a82745adc57eebf91916119bdfd1"},"schema_version":"1.0"},"canonical_sha256":"b58a9951bea84d3efa4e03d3e127198b1c71d633521d624e653d5758465badbd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:40.259087Z","signature_b64":"7+D8YDmJRuagBGaUGHvPPxxfY3cZn0CfVA/jInSL1a3epeqnGPZSSHg4Q5AhmcqRVMSHOAQ4CznuNtG3BcXKBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b58a9951bea84d3efa4e03d3e127198b1c71d633521d624e653d5758465badbd","last_reissued_at":"2026-05-18T00:06:40.258663Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:40.258663Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.00834","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":"2026-05-18T00:06:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ti2fEk5p73asS8B2g3Rj48+/y2k69md3LsDnUzPnV9WrT3LpglPNU7aXL4TVJsZQNN19YonW014+onholDybDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T04:23:03.406493Z"},"content_sha256":"7899f917263ab6025f1edac9accacae9bc2fd42b4d5602715630f1c1f7f60376","schema_version":"1.0","event_id":"sha256:7899f917263ab6025f1edac9accacae9bc2fd42b4d5602715630f1c1f7f60376"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:WWFJSUN6VBGT56SOAPJ6CJYZRM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Path integrals of a particle in a finite interval and on the half-line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Seiji Sakoda","submitted_at":"2018-04-03T06:00:48Z","abstract_excerpt":"We make use of point transformations to introduce new canonical variables for systems defined on a finite interval and on the half-line so that new position variables should take all real values from $-\\infty$ to $\\infty$. The completeness of eigenvectors of new momentum operators enables us to formulate time sliced path integrals for such systems. Short time kernels thus obtained require extension of the range of variables to the covering space in order to take all reflected paths into account. Upon this extension we determine phase factors attached to the amplitude for paths reflected at bou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.00834","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":"2026-05-18T00:06:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DQrxTYBTsU/W5Y5wGlJcDP3f0WhwKrPM2Ypm+XRc6Txx963ipGD1JTbHVPoYU1nBUPup+HRxKs2pyU6Q9o5FAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T04:23:03.406835Z"},"content_sha256":"31fe462d0b51a5780a32104103dc439038629aad223ea76c43294ea42712db63","schema_version":"1.0","event_id":"sha256:31fe462d0b51a5780a32104103dc439038629aad223ea76c43294ea42712db63"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WWFJSUN6VBGT56SOAPJ6CJYZRM/bundle.json","state_url":"https://pith.science/pith/WWFJSUN6VBGT56SOAPJ6CJYZRM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WWFJSUN6VBGT56SOAPJ6CJYZRM/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":"2026-06-03T04:23:03Z","links":{"resolver":"https://pith.science/pith/WWFJSUN6VBGT56SOAPJ6CJYZRM","bundle":"https://pith.science/pith/WWFJSUN6VBGT56SOAPJ6CJYZRM/bundle.json","state":"https://pith.science/pith/WWFJSUN6VBGT56SOAPJ6CJYZRM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WWFJSUN6VBGT56SOAPJ6CJYZRM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WWFJSUN6VBGT56SOAPJ6CJYZRM","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":"b9986321bbfc0187243ff028119e2bfa9a53a82745adc57eebf91916119bdfd1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-04-03T06:00:48Z","title_canon_sha256":"10a68e891314855b04b782685ceef9679938f22f8f35fefa8f9ef92cdeb32a67"},"schema_version":"1.0","source":{"id":"1804.00834","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.00834","created_at":"2026-05-18T00:06:40Z"},{"alias_kind":"arxiv_version","alias_value":"1804.00834v2","created_at":"2026-05-18T00:06:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.00834","created_at":"2026-05-18T00:06:40Z"},{"alias_kind":"pith_short_12","alias_value":"WWFJSUN6VBGT","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"WWFJSUN6VBGT56SO","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"WWFJSUN6","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:31fe462d0b51a5780a32104103dc439038629aad223ea76c43294ea42712db63","target":"graph","created_at":"2026-05-18T00:06:40Z","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 make use of point transformations to introduce new canonical variables for systems defined on a finite interval and on the half-line so that new position variables should take all real values from $-\\infty$ to $\\infty$. The completeness of eigenvectors of new momentum operators enables us to formulate time sliced path integrals for such systems. Short time kernels thus obtained require extension of the range of variables to the covering space in order to take all reflected paths into account. Upon this extension we determine phase factors attached to the amplitude for paths reflected at bou","authors_text":"Seiji Sakoda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-04-03T06:00:48Z","title":"Path integrals of a particle in a finite interval and on the half-line"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.00834","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":"sha256:7899f917263ab6025f1edac9accacae9bc2fd42b4d5602715630f1c1f7f60376","target":"record","created_at":"2026-05-18T00:06:40Z","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":"b9986321bbfc0187243ff028119e2bfa9a53a82745adc57eebf91916119bdfd1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-04-03T06:00:48Z","title_canon_sha256":"10a68e891314855b04b782685ceef9679938f22f8f35fefa8f9ef92cdeb32a67"},"schema_version":"1.0","source":{"id":"1804.00834","kind":"arxiv","version":2}},"canonical_sha256":"b58a9951bea84d3efa4e03d3e127198b1c71d633521d624e653d5758465badbd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b58a9951bea84d3efa4e03d3e127198b1c71d633521d624e653d5758465badbd","first_computed_at":"2026-05-18T00:06:40.258663Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:40.258663Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7+D8YDmJRuagBGaUGHvPPxxfY3cZn0CfVA/jInSL1a3epeqnGPZSSHg4Q5AhmcqRVMSHOAQ4CznuNtG3BcXKBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:40.259087Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.00834","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7899f917263ab6025f1edac9accacae9bc2fd42b4d5602715630f1c1f7f60376","sha256:31fe462d0b51a5780a32104103dc439038629aad223ea76c43294ea42712db63"],"state_sha256":"11742acbe7649c5357d04def47cdf7e811c1368639078446276eed60576b66e2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hsm6dmjfl1OX7H0KhGsdvbjGhxUs6QtkmsqzAJ2MjgHnlY26rrKP3VDdFLK9lZD2hlsfaS90wdkPj7KS8LOhAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T04:23:03.409134Z","bundle_sha256":"a5d919ab6aba849cfe06468260bac1a02fbdef78455ab8b2768b833c96a4f1ff"}}