{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:AHT4AZGI22I2BBTEAZKRMWSJAU","short_pith_number":"pith:AHT4AZGI","canonical_record":{"source":{"id":"1806.01220","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2018-06-04T17:00:59Z","cross_cats_sorted":["nucl-th"],"title_canon_sha256":"c733dc84da4edf30e469bc1fc17c8a2a741860907475b322310f21fb9900a83c","abstract_canon_sha256":"05b4b2dfaa2230ccb0f1ce40a90a38d445604627afe59d3cae98e458fa83e627"},"schema_version":"1.0"},"canonical_sha256":"01e7c064c8d691a086640655165a4905180eb919af52d75a85d74faa46d95ba2","source":{"kind":"arxiv","id":"1806.01220","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.01220","created_at":"2026-05-18T00:14:03Z"},{"alias_kind":"arxiv_version","alias_value":"1806.01220v1","created_at":"2026-05-18T00:14:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.01220","created_at":"2026-05-18T00:14:03Z"},{"alias_kind":"pith_short_12","alias_value":"AHT4AZGI22I2","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"AHT4AZGI22I2BBTE","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"AHT4AZGI","created_at":"2026-05-18T12:32:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:AHT4AZGI22I2BBTEAZKRMWSJAU","target":"record","payload":{"canonical_record":{"source":{"id":"1806.01220","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2018-06-04T17:00:59Z","cross_cats_sorted":["nucl-th"],"title_canon_sha256":"c733dc84da4edf30e469bc1fc17c8a2a741860907475b322310f21fb9900a83c","abstract_canon_sha256":"05b4b2dfaa2230ccb0f1ce40a90a38d445604627afe59d3cae98e458fa83e627"},"schema_version":"1.0"},"canonical_sha256":"01e7c064c8d691a086640655165a4905180eb919af52d75a85d74faa46d95ba2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:03.682158Z","signature_b64":"Jh6qifNv2CUY2AyG4pnnvcLmVM/Fu3H2xNPWhjDj77JDENPnrr+NBGoan6YZ8imrvi+L0CLLyHCtpaySc5J9Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01e7c064c8d691a086640655165a4905180eb919af52d75a85d74faa46d95ba2","last_reissued_at":"2026-05-18T00:14:03.681488Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:03.681488Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.01220","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":"2026-05-18T00:14:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sSDctbHSu6ALM3mWc/Z/w0zciJT8+J/c/ISZivZh3CYNfflX69wtvbxcv/o9UAyeN23fiqtWH6hKR65lfI2LBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:35:32.475993Z"},"content_sha256":"3c96c4fb78d04daefb4ad5afd41587f83cb58f2e988e6adfbf176512156a6b3e","schema_version":"1.0","event_id":"sha256:3c96c4fb78d04daefb4ad5afd41587f83cb58f2e988e6adfbf176512156a6b3e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:AHT4AZGI22I2BBTEAZKRMWSJAU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Momentum Sum Rule Is Violated in The Operator Product Expansion in QCD At The High Energy Colliders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nucl-th"],"primary_cat":"hep-ph","authors_text":"Gouranga C Nayak","submitted_at":"2018-06-04T17:00:59Z","abstract_excerpt":"To prove the momentum sum rule in the operator product expansion (OPE) in QCD at high energy colliders it is assumed that $<P| {\\hat T}^{++}(0)|P>=2(P^+)^2$ where $|P>$ is the momentum eigenstate of the hadron $H$ with momentum $P^\\mu$ and ${\\hat T}^{++}(0)$ is the $++$ component of the gauge invariant color singlet energy-momentum tensor density operator ${\\hat T}^{\\mu \\nu}(0)$ of all the quarks plus antiquarks plus gluons inside the hadron $H$. However, in this paper, we show that this relation $<P| {\\hat T}^{++}(0)|P>=2(P^+)^2$ is correct if ${\\hat T}^{\\mu \\nu}(0)$ is the energy-momentum te"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.01220","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":"2026-05-18T00:14:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gg8FCOBV/nGbQv0lHVml2pQ3/RMJVqk2lKnHO3QDYcp84S+QZu/gtkHPqqkHa5cNW1RbNYExYAq93vpo4GAsBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:35:32.476349Z"},"content_sha256":"b92450479980d68d1bd722830b45114fd9c0915d2c97a57dbb9d28ab1f7cba59","schema_version":"1.0","event_id":"sha256:b92450479980d68d1bd722830b45114fd9c0915d2c97a57dbb9d28ab1f7cba59"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AHT4AZGI22I2BBTEAZKRMWSJAU/bundle.json","state_url":"https://pith.science/pith/AHT4AZGI22I2BBTEAZKRMWSJAU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AHT4AZGI22I2BBTEAZKRMWSJAU/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":"2026-06-02T23:35:32Z","links":{"resolver":"https://pith.science/pith/AHT4AZGI22I2BBTEAZKRMWSJAU","bundle":"https://pith.science/pith/AHT4AZGI22I2BBTEAZKRMWSJAU/bundle.json","state":"https://pith.science/pith/AHT4AZGI22I2BBTEAZKRMWSJAU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AHT4AZGI22I2BBTEAZKRMWSJAU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:AHT4AZGI22I2BBTEAZKRMWSJAU","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":"05b4b2dfaa2230ccb0f1ce40a90a38d445604627afe59d3cae98e458fa83e627","cross_cats_sorted":["nucl-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2018-06-04T17:00:59Z","title_canon_sha256":"c733dc84da4edf30e469bc1fc17c8a2a741860907475b322310f21fb9900a83c"},"schema_version":"1.0","source":{"id":"1806.01220","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.01220","created_at":"2026-05-18T00:14:03Z"},{"alias_kind":"arxiv_version","alias_value":"1806.01220v1","created_at":"2026-05-18T00:14:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.01220","created_at":"2026-05-18T00:14:03Z"},{"alias_kind":"pith_short_12","alias_value":"AHT4AZGI22I2","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"AHT4AZGI22I2BBTE","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"AHT4AZGI","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:b92450479980d68d1bd722830b45114fd9c0915d2c97a57dbb9d28ab1f7cba59","target":"graph","created_at":"2026-05-18T00:14:03Z","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":"To prove the momentum sum rule in the operator product expansion (OPE) in QCD at high energy colliders it is assumed that $<P| {\\hat T}^{++}(0)|P>=2(P^+)^2$ where $|P>$ is the momentum eigenstate of the hadron $H$ with momentum $P^\\mu$ and ${\\hat T}^{++}(0)$ is the $++$ component of the gauge invariant color singlet energy-momentum tensor density operator ${\\hat T}^{\\mu \\nu}(0)$ of all the quarks plus antiquarks plus gluons inside the hadron $H$. However, in this paper, we show that this relation $<P| {\\hat T}^{++}(0)|P>=2(P^+)^2$ is correct if ${\\hat T}^{\\mu \\nu}(0)$ is the energy-momentum te","authors_text":"Gouranga C Nayak","cross_cats":["nucl-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2018-06-04T17:00:59Z","title":"Momentum Sum Rule Is Violated in The Operator Product Expansion in QCD At The High Energy Colliders"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.01220","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":"sha256:3c96c4fb78d04daefb4ad5afd41587f83cb58f2e988e6adfbf176512156a6b3e","target":"record","created_at":"2026-05-18T00:14:03Z","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":"05b4b2dfaa2230ccb0f1ce40a90a38d445604627afe59d3cae98e458fa83e627","cross_cats_sorted":["nucl-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2018-06-04T17:00:59Z","title_canon_sha256":"c733dc84da4edf30e469bc1fc17c8a2a741860907475b322310f21fb9900a83c"},"schema_version":"1.0","source":{"id":"1806.01220","kind":"arxiv","version":1}},"canonical_sha256":"01e7c064c8d691a086640655165a4905180eb919af52d75a85d74faa46d95ba2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01e7c064c8d691a086640655165a4905180eb919af52d75a85d74faa46d95ba2","first_computed_at":"2026-05-18T00:14:03.681488Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:03.681488Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Jh6qifNv2CUY2AyG4pnnvcLmVM/Fu3H2xNPWhjDj77JDENPnrr+NBGoan6YZ8imrvi+L0CLLyHCtpaySc5J9Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:03.682158Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.01220","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c96c4fb78d04daefb4ad5afd41587f83cb58f2e988e6adfbf176512156a6b3e","sha256:b92450479980d68d1bd722830b45114fd9c0915d2c97a57dbb9d28ab1f7cba59"],"state_sha256":"25a0153c6acc08bd83884680c1c9ba9435afd1a0bc1d1dd6573be609acee63c9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P5rpJGVrT1Upfz+8wxzn+pSFcgb2vE+IwbYT1arTjMjO9wv0MvihJSVVNq5PpwVekFJsxPrzHwwKS4Ei5kI5DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T23:35:32.478363Z","bundle_sha256":"a917e3371344cd49970d52e200841fe7e943d02bb0fe0808fcef9ada5098dd0a"}}