{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:6B34UFWZTZ3ZZWNJTUCZHLH4JD","short_pith_number":"pith:6B34UFWZ","canonical_record":{"source":{"id":"1203.2526","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-03-12T15:51:41Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"da0b657f01dc289d303396c4ad8b0475303d62068a5266a98342aa43287cf17f","abstract_canon_sha256":"fd1e4d44bc34f839479c49511fceb07bfc2ddc306dd159e8adde9d00b70762e2"},"schema_version":"1.0"},"canonical_sha256":"f077ca16d99e779cd9a99d0593acfc48fe9e907565ad23c4fd8bb60ce3fccbce","source":{"kind":"arxiv","id":"1203.2526","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.2526","created_at":"2026-05-18T04:00:02Z"},{"alias_kind":"arxiv_version","alias_value":"1203.2526v2","created_at":"2026-05-18T04:00:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.2526","created_at":"2026-05-18T04:00:02Z"},{"alias_kind":"pith_short_12","alias_value":"6B34UFWZTZ3Z","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6B34UFWZTZ3ZZWNJ","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6B34UFWZ","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:6B34UFWZTZ3ZZWNJTUCZHLH4JD","target":"record","payload":{"canonical_record":{"source":{"id":"1203.2526","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-03-12T15:51:41Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"da0b657f01dc289d303396c4ad8b0475303d62068a5266a98342aa43287cf17f","abstract_canon_sha256":"fd1e4d44bc34f839479c49511fceb07bfc2ddc306dd159e8adde9d00b70762e2"},"schema_version":"1.0"},"canonical_sha256":"f077ca16d99e779cd9a99d0593acfc48fe9e907565ad23c4fd8bb60ce3fccbce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:00:02.475759Z","signature_b64":"RhyYWIOW4/J40c29ftfIUiCa2XnI3SsgauyrkPK/nOEMUC5jQWgznitvYY8pyM2IKO41H+R2DTk7gIJf/dJrBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f077ca16d99e779cd9a99d0593acfc48fe9e907565ad23c4fd8bb60ce3fccbce","last_reissued_at":"2026-05-18T04:00:02.475081Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:00:02.475081Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.2526","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":"2026-05-18T04:00:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PCSDSWXpSL7n1axPqK7DaZsSovehn8YhWmCzWc2hES/V2kRHn/p8SpVcXbG/LjjH3YrlatfcdfX8wUVKHC49Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T07:50:10.211212Z"},"content_sha256":"187891733a52363a6249e3cc06a7834c0d5f83c666af1a0332f3f36b64432c26","schema_version":"1.0","event_id":"sha256:187891733a52363a6249e3cc06a7834c0d5f83c666af1a0332f3f36b64432c26"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:6B34UFWZTZ3ZZWNJTUCZHLH4JD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Dirac factorization method and the harmonic oscillator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"D. Babusci, G. Dattoli","submitted_at":"2012-03-12T15:51:41Z","abstract_excerpt":"We apply the Dirac factorization method to the nonrelativistic harmonic oscillator and, more in general, to Hamiltonians with a generic potential. It is shown that this procedure naturally leads to a supersymmetric formulation of the problems under study. It is also speculated on the physical meaning underlying this method and it is suggested that the vacuum field fluctuations can be viewed as the spontaneous emission of the associated two-level system, whose quantization is due to the noncommuting nature of the harmonic oscillator canonical variables."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2526","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":"2026-05-18T04:00:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o2ZTjha91ZkcU7Uh17HvrYgWnnw8AyA4g9dpnRpoZGebEy/mexzTuvAewUYdprICLiyzJ2cqeVRjhOe+crhUDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T07:50:10.211579Z"},"content_sha256":"eaec5858ff88fe65d2ac6b7892715093d4beb7b71cc9ee5375ff0227c405c412","schema_version":"1.0","event_id":"sha256:eaec5858ff88fe65d2ac6b7892715093d4beb7b71cc9ee5375ff0227c405c412"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6B34UFWZTZ3ZZWNJTUCZHLH4JD/bundle.json","state_url":"https://pith.science/pith/6B34UFWZTZ3ZZWNJTUCZHLH4JD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6B34UFWZTZ3ZZWNJTUCZHLH4JD/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":"2026-06-01T07:50:10Z","links":{"resolver":"https://pith.science/pith/6B34UFWZTZ3ZZWNJTUCZHLH4JD","bundle":"https://pith.science/pith/6B34UFWZTZ3ZZWNJTUCZHLH4JD/bundle.json","state":"https://pith.science/pith/6B34UFWZTZ3ZZWNJTUCZHLH4JD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6B34UFWZTZ3ZZWNJTUCZHLH4JD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6B34UFWZTZ3ZZWNJTUCZHLH4JD","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":"fd1e4d44bc34f839479c49511fceb07bfc2ddc306dd159e8adde9d00b70762e2","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-03-12T15:51:41Z","title_canon_sha256":"da0b657f01dc289d303396c4ad8b0475303d62068a5266a98342aa43287cf17f"},"schema_version":"1.0","source":{"id":"1203.2526","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.2526","created_at":"2026-05-18T04:00:02Z"},{"alias_kind":"arxiv_version","alias_value":"1203.2526v2","created_at":"2026-05-18T04:00:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.2526","created_at":"2026-05-18T04:00:02Z"},{"alias_kind":"pith_short_12","alias_value":"6B34UFWZTZ3Z","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6B34UFWZTZ3ZZWNJ","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6B34UFWZ","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:eaec5858ff88fe65d2ac6b7892715093d4beb7b71cc9ee5375ff0227c405c412","target":"graph","created_at":"2026-05-18T04:00:02Z","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 apply the Dirac factorization method to the nonrelativistic harmonic oscillator and, more in general, to Hamiltonians with a generic potential. It is shown that this procedure naturally leads to a supersymmetric formulation of the problems under study. It is also speculated on the physical meaning underlying this method and it is suggested that the vacuum field fluctuations can be viewed as the spontaneous emission of the associated two-level system, whose quantization is due to the noncommuting nature of the harmonic oscillator canonical variables.","authors_text":"D. Babusci, G. Dattoli","cross_cats":["hep-th","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-03-12T15:51:41Z","title":"The Dirac factorization method and the harmonic oscillator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2526","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":"sha256:187891733a52363a6249e3cc06a7834c0d5f83c666af1a0332f3f36b64432c26","target":"record","created_at":"2026-05-18T04:00:02Z","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":"fd1e4d44bc34f839479c49511fceb07bfc2ddc306dd159e8adde9d00b70762e2","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-03-12T15:51:41Z","title_canon_sha256":"da0b657f01dc289d303396c4ad8b0475303d62068a5266a98342aa43287cf17f"},"schema_version":"1.0","source":{"id":"1203.2526","kind":"arxiv","version":2}},"canonical_sha256":"f077ca16d99e779cd9a99d0593acfc48fe9e907565ad23c4fd8bb60ce3fccbce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f077ca16d99e779cd9a99d0593acfc48fe9e907565ad23c4fd8bb60ce3fccbce","first_computed_at":"2026-05-18T04:00:02.475081Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:00:02.475081Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RhyYWIOW4/J40c29ftfIUiCa2XnI3SsgauyrkPK/nOEMUC5jQWgznitvYY8pyM2IKO41H+R2DTk7gIJf/dJrBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:00:02.475759Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.2526","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:187891733a52363a6249e3cc06a7834c0d5f83c666af1a0332f3f36b64432c26","sha256:eaec5858ff88fe65d2ac6b7892715093d4beb7b71cc9ee5375ff0227c405c412"],"state_sha256":"e541e4a9ce4f9069370388d21dab57688f9fa634a13f0e3db442f49531cd21f7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ReTMv+9i/Okrg2r8jz7SPQqjEI1Vg5gVMyEdZEkfK2Hgfsm0UE/LDd2yeWEkVOG17MO1XkyLSKlW2gfwZmdgCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T07:50:10.213521Z","bundle_sha256":"a4671f019c816dd1617ded08c0f76fffeef56a59fbaef0a29f4e1a99da0c6856"}}