{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:N2NMTMQE2GAF4VHXTKTDVWOF7Y","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":"fa604b40ef928152060d6dab99259f25acdfac73172a238ac8dcc943db0725ce","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"hep-ph","submitted_at":"1999-07-26T14:15:48Z","title_canon_sha256":"2c116d997bfe3c9b0d667bd6fcae7574ba915dce571c7a887879cae5c92a0f44"},"schema_version":"1.0","source":{"id":"hep-ph/9907490","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-ph/9907490","created_at":"2026-05-18T01:38:55Z"},{"alias_kind":"arxiv_version","alias_value":"hep-ph/9907490v1","created_at":"2026-05-18T01:38:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-ph/9907490","created_at":"2026-05-18T01:38:55Z"},{"alias_kind":"pith_short_12","alias_value":"N2NMTMQE2GAF","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"N2NMTMQE2GAF4VHX","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"N2NMTMQE","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:835df5a313f1d052d1c2ea2009e2fd0c75c24a03861613fef3b78b078262b475","target":"graph","created_at":"2026-05-18T01:38:55Z","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":"Relations between integrals of time-ordered product of operators, and their representation in terms of energy-ordered products are studied. Both can be decomposed into irreducible factors and these relations are discussed as well. The energy-ordered representation was invented to separate various infrared contributions in gauge theories. It is shown that the irreducible time-ordered expressions can be used to accomplish the same purpose. Besides, it has the added advantage of being factorizable.","authors_text":"C.S. Lam","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"hep-ph","submitted_at":"1999-07-26T14:15:48Z","title":"Time Ordering, Energy Ordering, and Factorization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-ph/9907490","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:f7dc4bf4d9c707a3e0fdedf9b287e53e580c9319fdca25cb05e4a7d9dcd28092","target":"record","created_at":"2026-05-18T01:38:55Z","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":"fa604b40ef928152060d6dab99259f25acdfac73172a238ac8dcc943db0725ce","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"hep-ph","submitted_at":"1999-07-26T14:15:48Z","title_canon_sha256":"2c116d997bfe3c9b0d667bd6fcae7574ba915dce571c7a887879cae5c92a0f44"},"schema_version":"1.0","source":{"id":"hep-ph/9907490","kind":"arxiv","version":1}},"canonical_sha256":"6e9ac9b204d1805e54f79aa63ad9c5fe025562191e3b5e45af939fcf00c94161","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e9ac9b204d1805e54f79aa63ad9c5fe025562191e3b5e45af939fcf00c94161","first_computed_at":"2026-05-18T01:38:55.896675Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:55.896675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FQYwghXalh4uJbt6WfYyh8MNAcZ14ILPBHRoEw9S0Z/3hNW3stsJENcu7Kjd8gFfaIR+Jfgd7kMhFEOEdAexDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:55.897539Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-ph/9907490","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7dc4bf4d9c707a3e0fdedf9b287e53e580c9319fdca25cb05e4a7d9dcd28092","sha256:835df5a313f1d052d1c2ea2009e2fd0c75c24a03861613fef3b78b078262b475"],"state_sha256":"9c529a85644a993321f44cce51c3534701db47c911f4896b1297abe32374711b"}