{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:ZCODY65CFMC5KPBXA7GQQPALBE","short_pith_number":"pith:ZCODY65C","canonical_record":{"source":{"id":"1009.2313","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2010-09-13T07:31:41Z","cross_cats_sorted":[],"title_canon_sha256":"16504bbacca50de0ce9f59fd795fa8a8dcec163a364af269ebed0cd6ce06b954","abstract_canon_sha256":"aad1b7922028e2facb85577c18f63d43d14c79316c2dd040430514df973349ad"},"schema_version":"1.0"},"canonical_sha256":"c89c3c7ba22b05d53c3707cd083c0b090ed5838eb8d721449fcfe24f89f1f215","source":{"kind":"arxiv","id":"1009.2313","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.2313","created_at":"2026-05-18T04:26:13Z"},{"alias_kind":"arxiv_version","alias_value":"1009.2313v3","created_at":"2026-05-18T04:26:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.2313","created_at":"2026-05-18T04:26:13Z"},{"alias_kind":"pith_short_12","alias_value":"ZCODY65CFMC5","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"ZCODY65CFMC5KPBX","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"ZCODY65C","created_at":"2026-05-18T12:26:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:ZCODY65CFMC5KPBXA7GQQPALBE","target":"record","payload":{"canonical_record":{"source":{"id":"1009.2313","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2010-09-13T07:31:41Z","cross_cats_sorted":[],"title_canon_sha256":"16504bbacca50de0ce9f59fd795fa8a8dcec163a364af269ebed0cd6ce06b954","abstract_canon_sha256":"aad1b7922028e2facb85577c18f63d43d14c79316c2dd040430514df973349ad"},"schema_version":"1.0"},"canonical_sha256":"c89c3c7ba22b05d53c3707cd083c0b090ed5838eb8d721449fcfe24f89f1f215","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:26:13.328297Z","signature_b64":"WBH27yyDDVcY0Wxc+rfLJQ3yo1GlCxjlMySGVBz2Lzexyl+WBiQwx5nTEPci8Cr7EC0kFM2GEGXmEudk6EftCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c89c3c7ba22b05d53c3707cd083c0b090ed5838eb8d721449fcfe24f89f1f215","last_reissued_at":"2026-05-18T04:26:13.327769Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:26:13.327769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.2313","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:26:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mz1fiK4RcEPdmOetQ4TR2kvx4JpR7NKmYrsoLsNX7otxdR55fvK0BQUmmuCQwGC1NoqbPmaYbeDIjvgKaSHxBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:54:53.478576Z"},"content_sha256":"6c5c99d93a5e20a62327af446b2c5de4eaceb8cca1fd18877cf66f4cc0dd1c51","schema_version":"1.0","event_id":"sha256:6c5c99d93a5e20a62327af446b2c5de4eaceb8cca1fd18877cf66f4cc0dd1c51"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:ZCODY65CFMC5KPBXA7GQQPALBE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The hbar Expansion in Quantum Field Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Paul Hoyer, Stanley J. Brodsky","submitted_at":"2010-09-13T07:31:41Z","abstract_excerpt":"We show how expansions in powers of Planck's constant hbar = h/2\\pi can give new insights into perturbative and nonperturbative properties of quantum field theories. Since hbar is a fundamental parameter, exact Lorentz invariance and gauge invariance are maintained at each order of the expansion. The physics of the hbar expansion depends on the scheme; i.e., different expansions are obtained depending on which quantities (momenta, couplings and masses) are assumed to be independent of hbar. We show that if the coupling and mass parameters appearing in the Lagrangian density are taken to be ind"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2313","kind":"arxiv","version":3},"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":"2026-05-18T04:26:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d8gm5WB1RZ3i5JMV0YmdyA/AMGdnu462vBU6mgwo9sI9l5ABI68Q71gXkQfQxom/lTkB4uXiv8lNwV8mafYuAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:54:53.478966Z"},"content_sha256":"9022fc65bc13adf84f7e349d1bf90ea200c924074d98c61606176db62bd0c267","schema_version":"1.0","event_id":"sha256:9022fc65bc13adf84f7e349d1bf90ea200c924074d98c61606176db62bd0c267"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZCODY65CFMC5KPBXA7GQQPALBE/bundle.json","state_url":"https://pith.science/pith/ZCODY65CFMC5KPBXA7GQQPALBE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZCODY65CFMC5KPBXA7GQQPALBE/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":"2026-05-28T22:54:53Z","links":{"resolver":"https://pith.science/pith/ZCODY65CFMC5KPBXA7GQQPALBE","bundle":"https://pith.science/pith/ZCODY65CFMC5KPBXA7GQQPALBE/bundle.json","state":"https://pith.science/pith/ZCODY65CFMC5KPBXA7GQQPALBE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZCODY65CFMC5KPBXA7GQQPALBE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:ZCODY65CFMC5KPBXA7GQQPALBE","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":"aad1b7922028e2facb85577c18f63d43d14c79316c2dd040430514df973349ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2010-09-13T07:31:41Z","title_canon_sha256":"16504bbacca50de0ce9f59fd795fa8a8dcec163a364af269ebed0cd6ce06b954"},"schema_version":"1.0","source":{"id":"1009.2313","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.2313","created_at":"2026-05-18T04:26:13Z"},{"alias_kind":"arxiv_version","alias_value":"1009.2313v3","created_at":"2026-05-18T04:26:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.2313","created_at":"2026-05-18T04:26:13Z"},{"alias_kind":"pith_short_12","alias_value":"ZCODY65CFMC5","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"ZCODY65CFMC5KPBX","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"ZCODY65C","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:9022fc65bc13adf84f7e349d1bf90ea200c924074d98c61606176db62bd0c267","target":"graph","created_at":"2026-05-18T04:26:13Z","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 show how expansions in powers of Planck's constant hbar = h/2\\pi can give new insights into perturbative and nonperturbative properties of quantum field theories. Since hbar is a fundamental parameter, exact Lorentz invariance and gauge invariance are maintained at each order of the expansion. The physics of the hbar expansion depends on the scheme; i.e., different expansions are obtained depending on which quantities (momenta, couplings and masses) are assumed to be independent of hbar. We show that if the coupling and mass parameters appearing in the Lagrangian density are taken to be ind","authors_text":"Paul Hoyer, Stanley J. Brodsky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2010-09-13T07:31:41Z","title":"The hbar Expansion in Quantum Field Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2313","kind":"arxiv","version":3},"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":"sha256:6c5c99d93a5e20a62327af446b2c5de4eaceb8cca1fd18877cf66f4cc0dd1c51","target":"record","created_at":"2026-05-18T04:26:13Z","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":"aad1b7922028e2facb85577c18f63d43d14c79316c2dd040430514df973349ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2010-09-13T07:31:41Z","title_canon_sha256":"16504bbacca50de0ce9f59fd795fa8a8dcec163a364af269ebed0cd6ce06b954"},"schema_version":"1.0","source":{"id":"1009.2313","kind":"arxiv","version":3}},"canonical_sha256":"c89c3c7ba22b05d53c3707cd083c0b090ed5838eb8d721449fcfe24f89f1f215","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c89c3c7ba22b05d53c3707cd083c0b090ed5838eb8d721449fcfe24f89f1f215","first_computed_at":"2026-05-18T04:26:13.327769Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:26:13.327769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WBH27yyDDVcY0Wxc+rfLJQ3yo1GlCxjlMySGVBz2Lzexyl+WBiQwx5nTEPci8Cr7EC0kFM2GEGXmEudk6EftCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:26:13.328297Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.2313","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c5c99d93a5e20a62327af446b2c5de4eaceb8cca1fd18877cf66f4cc0dd1c51","sha256:9022fc65bc13adf84f7e349d1bf90ea200c924074d98c61606176db62bd0c267"],"state_sha256":"615dba12c295090ed37c45d57d8fa2c603dede680c8d3710cb69f4c9696388bc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nrpYTGWKy4ZQVB9FtrkzddCQd4pUix4srrNrzDaCGuVtGCeIwjG1PW+qWOUGblABJ/lzX7mzSZcidFtFe+zjDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T22:54:53.482634Z","bundle_sha256":"562b93b0df59357729681c2779498c3a6d1fd0cc3a894dbad99eed9770094cb5"}}