{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:WWP65XI4RZNQB7MKN64LYALNSM","short_pith_number":"pith:WWP65XI4","canonical_record":{"source":{"id":"1110.2624","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-12T10:25:08Z","cross_cats_sorted":["math.MP","nucl-th"],"title_canon_sha256":"efe0b9d2e920e0f47030600c7c0a4513be0def3cdd03347f8de1a95e4613f8d6","abstract_canon_sha256":"af5652b5e09d64a74605516a94bb5e2c3e40e56c16dab265e72db66b6abaf1e0"},"schema_version":"1.0"},"canonical_sha256":"b59feedd1c8e5b00fd8a6fb8bc016d931270ce48cfb99a03f1c8914c5dfed58f","source":{"kind":"arxiv","id":"1110.2624","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.2624","created_at":"2026-05-18T04:10:58Z"},{"alias_kind":"arxiv_version","alias_value":"1110.2624v1","created_at":"2026-05-18T04:10:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.2624","created_at":"2026-05-18T04:10:58Z"},{"alias_kind":"pith_short_12","alias_value":"WWP65XI4RZNQ","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WWP65XI4RZNQB7MK","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WWP65XI4","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:WWP65XI4RZNQB7MKN64LYALNSM","target":"record","payload":{"canonical_record":{"source":{"id":"1110.2624","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-12T10:25:08Z","cross_cats_sorted":["math.MP","nucl-th"],"title_canon_sha256":"efe0b9d2e920e0f47030600c7c0a4513be0def3cdd03347f8de1a95e4613f8d6","abstract_canon_sha256":"af5652b5e09d64a74605516a94bb5e2c3e40e56c16dab265e72db66b6abaf1e0"},"schema_version":"1.0"},"canonical_sha256":"b59feedd1c8e5b00fd8a6fb8bc016d931270ce48cfb99a03f1c8914c5dfed58f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:58.286570Z","signature_b64":"u7ptp79eIrEfLgUvgEx0IMAvYb+bkpxCDnIm5mFmrsHhyxU8YsrbHDtOFC7N2Gnm8AUYJMMAHcMnTgisT27cCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b59feedd1c8e5b00fd8a6fb8bc016d931270ce48cfb99a03f1c8914c5dfed58f","last_reissued_at":"2026-05-18T04:10:58.286055Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:58.286055Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.2624","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":"2026-05-18T04:10:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/hQfl/wOYeDD+VoBeEA0jW/mZq0lYUHJeRaieUL/gj2vLdjnBRpRSn6LlaHJMUsVsUgkSIEwEjdDHekxfgl+Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:40:14.901764Z"},"content_sha256":"b1b0724c1452dc083844e6330867f8e07e9ae36e58eafb382d09514d1a883edd","schema_version":"1.0","event_id":"sha256:b1b0724c1452dc083844e6330867f8e07e9ae36e58eafb382d09514d1a883edd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:WWP65XI4RZNQB7MKN64LYALNSM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantization on Space-Time Hyperboloids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","nucl-th"],"primary_cat":"math-ph","authors_text":"Elmar P. Biernat","submitted_at":"2011-10-12T10:25:08Z","abstract_excerpt":"We quantize a relativistic massive complex spin-0 field and a relativistic massive spin-1/2 field on a space-time hyperboloid. We call this procedure point-form canonical quantization. Lorentz invariance of the hyperboloid implies that the 4 generators for translations become dynamic and interaction dependent, whereas the 6 generators for Lorentz transformations remain kinematic and interaction free. We expand the fields in terms of usual plane waves and prove the equivalence to equal-time quantization by representing the Poincare generators in a momentum basis. We formulate a generalized scat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2624","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":""},"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":"2026-05-18T04:10:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5mvKhzN4CNbX3nl5ksRyt27Njt5BKydczv5WzAmoi0A54oNUa8LaiqU+U0AXILnNBogSSfQsEpfxNCxyYDPXDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:40:14.902487Z"},"content_sha256":"a6c464af568baccf87a5b312141611bfb41bd7678b8731814abd6db0a756c069","schema_version":"1.0","event_id":"sha256:a6c464af568baccf87a5b312141611bfb41bd7678b8731814abd6db0a756c069"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WWP65XI4RZNQB7MKN64LYALNSM/bundle.json","state_url":"https://pith.science/pith/WWP65XI4RZNQB7MKN64LYALNSM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WWP65XI4RZNQB7MKN64LYALNSM/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":"2026-06-09T06:40:14Z","links":{"resolver":"https://pith.science/pith/WWP65XI4RZNQB7MKN64LYALNSM","bundle":"https://pith.science/pith/WWP65XI4RZNQB7MKN64LYALNSM/bundle.json","state":"https://pith.science/pith/WWP65XI4RZNQB7MKN64LYALNSM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WWP65XI4RZNQB7MKN64LYALNSM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:WWP65XI4RZNQB7MKN64LYALNSM","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":"af5652b5e09d64a74605516a94bb5e2c3e40e56c16dab265e72db66b6abaf1e0","cross_cats_sorted":["math.MP","nucl-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-12T10:25:08Z","title_canon_sha256":"efe0b9d2e920e0f47030600c7c0a4513be0def3cdd03347f8de1a95e4613f8d6"},"schema_version":"1.0","source":{"id":"1110.2624","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.2624","created_at":"2026-05-18T04:10:58Z"},{"alias_kind":"arxiv_version","alias_value":"1110.2624v1","created_at":"2026-05-18T04:10:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.2624","created_at":"2026-05-18T04:10:58Z"},{"alias_kind":"pith_short_12","alias_value":"WWP65XI4RZNQ","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WWP65XI4RZNQB7MK","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WWP65XI4","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:a6c464af568baccf87a5b312141611bfb41bd7678b8731814abd6db0a756c069","target":"graph","created_at":"2026-05-18T04:10:58Z","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 quantize a relativistic massive complex spin-0 field and a relativistic massive spin-1/2 field on a space-time hyperboloid. We call this procedure point-form canonical quantization. Lorentz invariance of the hyperboloid implies that the 4 generators for translations become dynamic and interaction dependent, whereas the 6 generators for Lorentz transformations remain kinematic and interaction free. We expand the fields in terms of usual plane waves and prove the equivalence to equal-time quantization by representing the Poincare generators in a momentum basis. We formulate a generalized scat","authors_text":"Elmar P. Biernat","cross_cats":["math.MP","nucl-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-12T10:25:08Z","title":"Quantization on Space-Time Hyperboloids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2624","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:b1b0724c1452dc083844e6330867f8e07e9ae36e58eafb382d09514d1a883edd","target":"record","created_at":"2026-05-18T04:10:58Z","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":"af5652b5e09d64a74605516a94bb5e2c3e40e56c16dab265e72db66b6abaf1e0","cross_cats_sorted":["math.MP","nucl-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-12T10:25:08Z","title_canon_sha256":"efe0b9d2e920e0f47030600c7c0a4513be0def3cdd03347f8de1a95e4613f8d6"},"schema_version":"1.0","source":{"id":"1110.2624","kind":"arxiv","version":1}},"canonical_sha256":"b59feedd1c8e5b00fd8a6fb8bc016d931270ce48cfb99a03f1c8914c5dfed58f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b59feedd1c8e5b00fd8a6fb8bc016d931270ce48cfb99a03f1c8914c5dfed58f","first_computed_at":"2026-05-18T04:10:58.286055Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:58.286055Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u7ptp79eIrEfLgUvgEx0IMAvYb+bkpxCDnIm5mFmrsHhyxU8YsrbHDtOFC7N2Gnm8AUYJMMAHcMnTgisT27cCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:58.286570Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.2624","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b1b0724c1452dc083844e6330867f8e07e9ae36e58eafb382d09514d1a883edd","sha256:a6c464af568baccf87a5b312141611bfb41bd7678b8731814abd6db0a756c069"],"state_sha256":"aa86e35a0c6d3ee95508c88c07e9e41bfeb622da27684e82aeadc713775494b4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eQeiDydlE4JpiwBP0ocxbO1Rq/GDKa3DD42BovxI9SkLEXBOZ8WIa28dR7qDh+j0LxbftNfTlJuRzv35P/x+Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T06:40:14.906894Z","bundle_sha256":"f69dba92d60420792bcbb524d476accb4cfd0a2e3476fc86a4003b9aadb2bcbc"}}