{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:YC3QBW4774SJUFDJLXLXOI25PU","short_pith_number":"pith:YC3QBW47","canonical_record":{"source":{"id":"2204.13119","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-04-27T18:00:01Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"e82a5f92a5fabaca5f1194f9d02f294f81238e6e4e8e003e45dbb538831a6a6e","abstract_canon_sha256":"0929cd4b27a827ac8605919ba183dc03c7e932a291bd8680a988a45970d0a38d"},"schema_version":"1.0"},"canonical_sha256":"c0b700db9fff249a14695dd777235d7d2fc6b10d501bef4fa46afc92cbcabd81","source":{"kind":"arxiv","id":"2204.13119","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2204.13119","created_at":"2026-07-05T05:21:25Z"},{"alias_kind":"arxiv_version","alias_value":"2204.13119v2","created_at":"2026-07-05T05:21:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.13119","created_at":"2026-07-05T05:21:25Z"},{"alias_kind":"pith_short_12","alias_value":"YC3QBW4774SJ","created_at":"2026-07-05T05:21:25Z"},{"alias_kind":"pith_short_16","alias_value":"YC3QBW4774SJUFDJ","created_at":"2026-07-05T05:21:25Z"},{"alias_kind":"pith_short_8","alias_value":"YC3QBW47","created_at":"2026-07-05T05:21:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:YC3QBW4774SJUFDJLXLXOI25PU","target":"record","payload":{"canonical_record":{"source":{"id":"2204.13119","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-04-27T18:00:01Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"e82a5f92a5fabaca5f1194f9d02f294f81238e6e4e8e003e45dbb538831a6a6e","abstract_canon_sha256":"0929cd4b27a827ac8605919ba183dc03c7e932a291bd8680a988a45970d0a38d"},"schema_version":"1.0"},"canonical_sha256":"c0b700db9fff249a14695dd777235d7d2fc6b10d501bef4fa46afc92cbcabd81","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:21:25.057880Z","signature_b64":"vX9ktE18C0KZR259PYEt5wIe4NrBkOPpui+Au3AVjEFI/jpq/ybQIZMvKTQ6MNqEXWoQ7WuxC3mjHYb9ywQ4Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c0b700db9fff249a14695dd777235d7d2fc6b10d501bef4fa46afc92cbcabd81","last_reissued_at":"2026-07-05T05:21:25.057383Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:21:25.057383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2204.13119","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":"2026-07-05T05:21:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8LoSteEwD312hAj++CUkH7M24nl32u0ram9lKjIistWYeUR4Rgiya5F+GXPUpeqzegBxsWUFyQmBdSL6ZZzbBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T19:53:05.670320Z"},"content_sha256":"a85bd66f1be33e4f816f5634fefe9e28c0e962e24db86410e3b88e02c9cb1b02","schema_version":"1.0","event_id":"sha256:a85bd66f1be33e4f816f5634fefe9e28c0e962e24db86410e3b88e02c9cb1b02"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:YC3QBW4774SJUFDJLXLXOI25PU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gauge invariance from on-shell massive amplitudes and tree unitarity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph"],"primary_cat":"hep-th","authors_text":"Da Liu, Zhewei Yin","submitted_at":"2022-04-27T18:00:01Z","abstract_excerpt":"We study the three-particle and four-particle scattering amplitudes for an arbitrary, finite number of massive scalars, spinors and vectors by employing the on-shell massive spinor formalism. We consider the most general three-particle amplitudes with energy growing behavior at most of $\\mathcal{O} (E)$. This is the special case of the requirement of tree unitarity, which states that the $N$-particle scattering amplitudes at tree-level should grow at most as $\\mathcal{O} (E^{4-N})$ in the high energy hard scattering limit, i.e. at fixed non-zero angles. Then the factorizable parts of the four-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.13119","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2204.13119/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T05:21:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9Rypm/GaRoCYx2dP2TXAVv/By+4BBKSarhwdgaqLwZ8bzwMxCxrKNYHpOPT6YWEsNBI7eLJO5syZCz5htyhSBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T19:53:05.670870Z"},"content_sha256":"1f8a93f07b626ffb472e627e9b8be901741ba0805b3149c022c8c6b515716e16","schema_version":"1.0","event_id":"sha256:1f8a93f07b626ffb472e627e9b8be901741ba0805b3149c022c8c6b515716e16"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YC3QBW4774SJUFDJLXLXOI25PU/bundle.json","state_url":"https://pith.science/pith/YC3QBW4774SJUFDJLXLXOI25PU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YC3QBW4774SJUFDJLXLXOI25PU/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":"2026-08-09T19:53:05Z","links":{"resolver":"https://pith.science/pith/YC3QBW4774SJUFDJLXLXOI25PU","bundle":"https://pith.science/pith/YC3QBW4774SJUFDJLXLXOI25PU/bundle.json","state":"https://pith.science/pith/YC3QBW4774SJUFDJLXLXOI25PU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YC3QBW4774SJUFDJLXLXOI25PU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:YC3QBW4774SJUFDJLXLXOI25PU","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":"0929cd4b27a827ac8605919ba183dc03c7e932a291bd8680a988a45970d0a38d","cross_cats_sorted":["hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-04-27T18:00:01Z","title_canon_sha256":"e82a5f92a5fabaca5f1194f9d02f294f81238e6e4e8e003e45dbb538831a6a6e"},"schema_version":"1.0","source":{"id":"2204.13119","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2204.13119","created_at":"2026-07-05T05:21:25Z"},{"alias_kind":"arxiv_version","alias_value":"2204.13119v2","created_at":"2026-07-05T05:21:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.13119","created_at":"2026-07-05T05:21:25Z"},{"alias_kind":"pith_short_12","alias_value":"YC3QBW4774SJ","created_at":"2026-07-05T05:21:25Z"},{"alias_kind":"pith_short_16","alias_value":"YC3QBW4774SJUFDJ","created_at":"2026-07-05T05:21:25Z"},{"alias_kind":"pith_short_8","alias_value":"YC3QBW47","created_at":"2026-07-05T05:21:25Z"}],"graph_snapshots":[{"event_id":"sha256:1f8a93f07b626ffb472e627e9b8be901741ba0805b3149c022c8c6b515716e16","target":"graph","created_at":"2026-07-05T05:21:25Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2204.13119/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the three-particle and four-particle scattering amplitudes for an arbitrary, finite number of massive scalars, spinors and vectors by employing the on-shell massive spinor formalism. We consider the most general three-particle amplitudes with energy growing behavior at most of $\\mathcal{O} (E)$. This is the special case of the requirement of tree unitarity, which states that the $N$-particle scattering amplitudes at tree-level should grow at most as $\\mathcal{O} (E^{4-N})$ in the high energy hard scattering limit, i.e. at fixed non-zero angles. Then the factorizable parts of the four-","authors_text":"Da Liu, Zhewei Yin","cross_cats":["hep-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-04-27T18:00:01Z","title":"Gauge invariance from on-shell massive amplitudes and tree unitarity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.13119","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:a85bd66f1be33e4f816f5634fefe9e28c0e962e24db86410e3b88e02c9cb1b02","target":"record","created_at":"2026-07-05T05:21:25Z","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":"0929cd4b27a827ac8605919ba183dc03c7e932a291bd8680a988a45970d0a38d","cross_cats_sorted":["hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-04-27T18:00:01Z","title_canon_sha256":"e82a5f92a5fabaca5f1194f9d02f294f81238e6e4e8e003e45dbb538831a6a6e"},"schema_version":"1.0","source":{"id":"2204.13119","kind":"arxiv","version":2}},"canonical_sha256":"c0b700db9fff249a14695dd777235d7d2fc6b10d501bef4fa46afc92cbcabd81","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c0b700db9fff249a14695dd777235d7d2fc6b10d501bef4fa46afc92cbcabd81","first_computed_at":"2026-07-05T05:21:25.057383Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:21:25.057383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vX9ktE18C0KZR259PYEt5wIe4NrBkOPpui+Au3AVjEFI/jpq/ybQIZMvKTQ6MNqEXWoQ7WuxC3mjHYb9ywQ4Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:21:25.057880Z","signed_message":"canonical_sha256_bytes"},"source_id":"2204.13119","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a85bd66f1be33e4f816f5634fefe9e28c0e962e24db86410e3b88e02c9cb1b02","sha256:1f8a93f07b626ffb472e627e9b8be901741ba0805b3149c022c8c6b515716e16"],"state_sha256":"bcb4ee5472ec20eedba390c75b551d253c6ebb90a70347c816a78f851083d321"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9NjmS48KJ6EwrGitaMFC9Lpu4BYoHY9ey5dl+9IeFWAmMTY98cfZmDvc0qwhSO4wiNPm4r43m1wOgGLO4aSzBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T19:53:05.676339Z","bundle_sha256":"8707677b4e835e82f73c37b4cc677bca2d9c3658e4c852814ce76c5a399cb570"}}