{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:62UHCZRQLTAVWE3GJHHK663XSM","short_pith_number":"pith:62UHCZRQ","canonical_record":{"source":{"id":"1809.10406","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2018-09-27T08:41:49Z","cross_cats_sorted":[],"title_canon_sha256":"1409713e4ee38aa3ced0693d6ebc394d2d3baec57ce0418606ad44c9c02eb9bc","abstract_canon_sha256":"f871ee0e9839dc330e0e734285eaf9f2ae62b6fe8ccddbc299f9fda2ca20f3d0"},"schema_version":"1.0"},"canonical_sha256":"f6a87166305cc15b136649ceaf7b77930e7d74831962cea89bf5361bef32c04d","source":{"kind":"arxiv","id":"1809.10406","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.10406","created_at":"2026-05-17T23:59:57Z"},{"alias_kind":"arxiv_version","alias_value":"1809.10406v2","created_at":"2026-05-17T23:59:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.10406","created_at":"2026-05-17T23:59:57Z"},{"alias_kind":"pith_short_12","alias_value":"62UHCZRQLTAV","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"62UHCZRQLTAVWE3G","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"62UHCZRQ","created_at":"2026-05-18T12:32:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:62UHCZRQLTAVWE3GJHHK663XSM","target":"record","payload":{"canonical_record":{"source":{"id":"1809.10406","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2018-09-27T08:41:49Z","cross_cats_sorted":[],"title_canon_sha256":"1409713e4ee38aa3ced0693d6ebc394d2d3baec57ce0418606ad44c9c02eb9bc","abstract_canon_sha256":"f871ee0e9839dc330e0e734285eaf9f2ae62b6fe8ccddbc299f9fda2ca20f3d0"},"schema_version":"1.0"},"canonical_sha256":"f6a87166305cc15b136649ceaf7b77930e7d74831962cea89bf5361bef32c04d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:57.634579Z","signature_b64":"jZOqHpBRba+E6ZBToUt7dg7fq9GMaFrxa0ReV8XSR/ug53M5ZmfV76EDNYNTyx0nAzWDme90B5UFYCiGKAMEAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6a87166305cc15b136649ceaf7b77930e7d74831962cea89bf5361bef32c04d","last_reissued_at":"2026-05-17T23:59:57.633885Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:57.633885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.10406","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":"2026-05-17T23:59:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M11Wm4NH2cfLl0Wwgu2gneny7oG/CS4LFPZEmpCSeuIPj2h2nusGUfAvawqagTeLpWNtB8QdXIp2l5qAj7w5Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:26:59.741117Z"},"content_sha256":"cfdd8811ddbff10c795b8cdfc02ec3adba82f9d6ef39c365bb5f221669a5f9b3","schema_version":"1.0","event_id":"sha256:cfdd8811ddbff10c795b8cdfc02ec3adba82f9d6ef39c365bb5f221669a5f9b3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:62UHCZRQLTAVWE3GJHHK663XSM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Black disk radius constrained by unitarity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"A.D. Martin, M.G. Ryskin, V.A. Khoze","submitted_at":"2018-09-27T08:41:49Z","abstract_excerpt":"We argue that if the elastic proton-proton cross section increases with energy, the Froissart-like high energy behaviour of the elastic amplitude (which corresponds to a `black disk' of radius $R(s)=c\\ln s-\\beta\\ln(\\ln s)$) is the only possibility to satisfy the unitarity equation at each value of the impact parameter, $b$. Otherwise the cross section of events with Large Rapidity Gaps grows faster than the total cross section at the same $b$. That is, these `gap' events require {\\it maximal} growth of the high-energy (asymptotic) cross section and of the interaction radius $R(s)$ in order to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10406","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":""},"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":"2026-05-17T23:59:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+hhNCAihTn8ZRlsfQC6mHNsM/rRa35+00qmEdbFwR9dZi6IttD87gcB4pZJ0v2pMSjzo2hfSR6kdsLA/+s0sDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:26:59.741859Z"},"content_sha256":"3784fcc554f66946b7b44f2df44b6652d2c2dc6fe13773a8e83be4fae27c62be","schema_version":"1.0","event_id":"sha256:3784fcc554f66946b7b44f2df44b6652d2c2dc6fe13773a8e83be4fae27c62be"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/62UHCZRQLTAVWE3GJHHK663XSM/bundle.json","state_url":"https://pith.science/pith/62UHCZRQLTAVWE3GJHHK663XSM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/62UHCZRQLTAVWE3GJHHK663XSM/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":"2026-05-31T05:26:59Z","links":{"resolver":"https://pith.science/pith/62UHCZRQLTAVWE3GJHHK663XSM","bundle":"https://pith.science/pith/62UHCZRQLTAVWE3GJHHK663XSM/bundle.json","state":"https://pith.science/pith/62UHCZRQLTAVWE3GJHHK663XSM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/62UHCZRQLTAVWE3GJHHK663XSM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:62UHCZRQLTAVWE3GJHHK663XSM","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":"f871ee0e9839dc330e0e734285eaf9f2ae62b6fe8ccddbc299f9fda2ca20f3d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2018-09-27T08:41:49Z","title_canon_sha256":"1409713e4ee38aa3ced0693d6ebc394d2d3baec57ce0418606ad44c9c02eb9bc"},"schema_version":"1.0","source":{"id":"1809.10406","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.10406","created_at":"2026-05-17T23:59:57Z"},{"alias_kind":"arxiv_version","alias_value":"1809.10406v2","created_at":"2026-05-17T23:59:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.10406","created_at":"2026-05-17T23:59:57Z"},{"alias_kind":"pith_short_12","alias_value":"62UHCZRQLTAV","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"62UHCZRQLTAVWE3G","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"62UHCZRQ","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:3784fcc554f66946b7b44f2df44b6652d2c2dc6fe13773a8e83be4fae27c62be","target":"graph","created_at":"2026-05-17T23:59:57Z","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 argue that if the elastic proton-proton cross section increases with energy, the Froissart-like high energy behaviour of the elastic amplitude (which corresponds to a `black disk' of radius $R(s)=c\\ln s-\\beta\\ln(\\ln s)$) is the only possibility to satisfy the unitarity equation at each value of the impact parameter, $b$. Otherwise the cross section of events with Large Rapidity Gaps grows faster than the total cross section at the same $b$. That is, these `gap' events require {\\it maximal} growth of the high-energy (asymptotic) cross section and of the interaction radius $R(s)$ in order to ","authors_text":"A.D. Martin, M.G. Ryskin, V.A. Khoze","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2018-09-27T08:41:49Z","title":"Black disk radius constrained by unitarity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10406","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:cfdd8811ddbff10c795b8cdfc02ec3adba82f9d6ef39c365bb5f221669a5f9b3","target":"record","created_at":"2026-05-17T23:59:57Z","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":"f871ee0e9839dc330e0e734285eaf9f2ae62b6fe8ccddbc299f9fda2ca20f3d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2018-09-27T08:41:49Z","title_canon_sha256":"1409713e4ee38aa3ced0693d6ebc394d2d3baec57ce0418606ad44c9c02eb9bc"},"schema_version":"1.0","source":{"id":"1809.10406","kind":"arxiv","version":2}},"canonical_sha256":"f6a87166305cc15b136649ceaf7b77930e7d74831962cea89bf5361bef32c04d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6a87166305cc15b136649ceaf7b77930e7d74831962cea89bf5361bef32c04d","first_computed_at":"2026-05-17T23:59:57.633885Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:57.633885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jZOqHpBRba+E6ZBToUt7dg7fq9GMaFrxa0ReV8XSR/ug53M5ZmfV76EDNYNTyx0nAzWDme90B5UFYCiGKAMEAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:57.634579Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.10406","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cfdd8811ddbff10c795b8cdfc02ec3adba82f9d6ef39c365bb5f221669a5f9b3","sha256:3784fcc554f66946b7b44f2df44b6652d2c2dc6fe13773a8e83be4fae27c62be"],"state_sha256":"abce5d78a597fa60a42170cf8a31f293e9d24f77d482d740e061fabe8fc5574c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nFah46LTWIcmodOnERlaI394aeR9zMgqvF5XMjcpfzoBDcP49D+OO+W7FSBJd5EhpoRlYx5KX3ufDoLxt+5IDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T05:26:59.745992Z","bundle_sha256":"826a88b49be3ecebf64f6a4a314825f19d78f63ed754e49348b191002bd22cd8"}}