{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:GIR2F24WONQUS4GAKTYYS7LZ2A","short_pith_number":"pith:GIR2F24W","canonical_record":{"source":{"id":"1506.07201","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2015-06-23T21:14:18Z","cross_cats_sorted":[],"title_canon_sha256":"8e715a1aa3bef170c7795859bb54c156c7ec069859d9c074238fa99387a1c839","abstract_canon_sha256":"f74ed5a8c9cb1aae7c8fe6115318f74dff5773f82a5a49bae2b35fbecd1d9ad0"},"schema_version":"1.0"},"canonical_sha256":"3223a2eb9673614970c054f1897d79d002ea334c4e4cede646671c6db476fb62","source":{"kind":"arxiv","id":"1506.07201","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.07201","created_at":"2026-05-17T23:49:53Z"},{"alias_kind":"arxiv_version","alias_value":"1506.07201v1","created_at":"2026-05-17T23:49:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.07201","created_at":"2026-05-17T23:49:53Z"},{"alias_kind":"pith_short_12","alias_value":"GIR2F24WONQU","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GIR2F24WONQUS4GA","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GIR2F24W","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:GIR2F24WONQUS4GAKTYYS7LZ2A","target":"record","payload":{"canonical_record":{"source":{"id":"1506.07201","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2015-06-23T21:14:18Z","cross_cats_sorted":[],"title_canon_sha256":"8e715a1aa3bef170c7795859bb54c156c7ec069859d9c074238fa99387a1c839","abstract_canon_sha256":"f74ed5a8c9cb1aae7c8fe6115318f74dff5773f82a5a49bae2b35fbecd1d9ad0"},"schema_version":"1.0"},"canonical_sha256":"3223a2eb9673614970c054f1897d79d002ea334c4e4cede646671c6db476fb62","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:53.441245Z","signature_b64":"0dX7FFA5NcIntwnnzEc3FnKjwFKihUKdeoZFoJs29q9ElYimOqSs/trgez2E+J8aWDOCwwvr5+2PD9XyeqA+BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3223a2eb9673614970c054f1897d79d002ea334c4e4cede646671c6db476fb62","last_reissued_at":"2026-05-17T23:49:53.440789Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:53.440789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.07201","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":"2026-05-17T23:49:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bJ6JhzmWaDj683+tCdKWhqvUw2SyxPwALdGnTxujF7IIRYgcWOKxCxQ4LSB0cVC6SV0UkLckwxJHI3qZv7e+Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T20:53:24.393832Z"},"content_sha256":"79de98246cbd026406432f36538762c10f372ba11fca968f407e044ff1c3c906","schema_version":"1.0","event_id":"sha256:79de98246cbd026406432f36538762c10f372ba11fca968f407e044ff1c3c906"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:GIR2F24WONQUS4GAKTYYS7LZ2A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"anQCD: Fortran programs for couplings at complex momenta in various analytic QCD models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Cesar Ayala, Gorazd Cvetic","submitted_at":"2015-06-23T21:14:18Z","abstract_excerpt":"We provide three Fortran programs which evaluate the QCD analytic (holomorphic) couplings $\\mathcal{A}_{\\nu}(Q^2)$ for complex or real squared momenta $Q^2$. These couplings are holomorphic analogs of the powers $a(Q^2)^{\\nu}$ of the underlying perturbative QCD (pQCD) coupling $a(Q^2) \\equiv \\alpha_s(Q^2)/\\pi$, in three analytic QCD models (anQCD): Fractional Analytic Perturbation Theory (FAPT), Two-delta analytic QCD (2$\\delta$anQCD), and Massive Perturbation Theory (MPT). The index $\\nu$ can be noninteger. The provided programs do basically the same job as the Mathematica package anQCD.m in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07201","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":"2026-05-17T23:49:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YX1e2s6o3UM6DgcAL2ZApxbleUrc7TQ7btyvWSmU4olQ4xwFfr+X1L+A2euglUWHW9vMAlsdXYV1qImdys4KAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T20:53:24.394192Z"},"content_sha256":"d9a4f9658aba82d93a88e4d2d3c3c732428ca14282ed20621d61a78d42bf4b92","schema_version":"1.0","event_id":"sha256:d9a4f9658aba82d93a88e4d2d3c3c732428ca14282ed20621d61a78d42bf4b92"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GIR2F24WONQUS4GAKTYYS7LZ2A/bundle.json","state_url":"https://pith.science/pith/GIR2F24WONQUS4GAKTYYS7LZ2A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GIR2F24WONQUS4GAKTYYS7LZ2A/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":"2026-06-02T20:53:24Z","links":{"resolver":"https://pith.science/pith/GIR2F24WONQUS4GAKTYYS7LZ2A","bundle":"https://pith.science/pith/GIR2F24WONQUS4GAKTYYS7LZ2A/bundle.json","state":"https://pith.science/pith/GIR2F24WONQUS4GAKTYYS7LZ2A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GIR2F24WONQUS4GAKTYYS7LZ2A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GIR2F24WONQUS4GAKTYYS7LZ2A","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":"f74ed5a8c9cb1aae7c8fe6115318f74dff5773f82a5a49bae2b35fbecd1d9ad0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2015-06-23T21:14:18Z","title_canon_sha256":"8e715a1aa3bef170c7795859bb54c156c7ec069859d9c074238fa99387a1c839"},"schema_version":"1.0","source":{"id":"1506.07201","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.07201","created_at":"2026-05-17T23:49:53Z"},{"alias_kind":"arxiv_version","alias_value":"1506.07201v1","created_at":"2026-05-17T23:49:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.07201","created_at":"2026-05-17T23:49:53Z"},{"alias_kind":"pith_short_12","alias_value":"GIR2F24WONQU","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GIR2F24WONQUS4GA","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GIR2F24W","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:d9a4f9658aba82d93a88e4d2d3c3c732428ca14282ed20621d61a78d42bf4b92","target":"graph","created_at":"2026-05-17T23:49:53Z","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 provide three Fortran programs which evaluate the QCD analytic (holomorphic) couplings $\\mathcal{A}_{\\nu}(Q^2)$ for complex or real squared momenta $Q^2$. These couplings are holomorphic analogs of the powers $a(Q^2)^{\\nu}$ of the underlying perturbative QCD (pQCD) coupling $a(Q^2) \\equiv \\alpha_s(Q^2)/\\pi$, in three analytic QCD models (anQCD): Fractional Analytic Perturbation Theory (FAPT), Two-delta analytic QCD (2$\\delta$anQCD), and Massive Perturbation Theory (MPT). The index $\\nu$ can be noninteger. The provided programs do basically the same job as the Mathematica package anQCD.m in ","authors_text":"Cesar Ayala, Gorazd Cvetic","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2015-06-23T21:14:18Z","title":"anQCD: Fortran programs for couplings at complex momenta in various analytic QCD models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07201","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":"sha256:79de98246cbd026406432f36538762c10f372ba11fca968f407e044ff1c3c906","target":"record","created_at":"2026-05-17T23:49:53Z","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":"f74ed5a8c9cb1aae7c8fe6115318f74dff5773f82a5a49bae2b35fbecd1d9ad0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2015-06-23T21:14:18Z","title_canon_sha256":"8e715a1aa3bef170c7795859bb54c156c7ec069859d9c074238fa99387a1c839"},"schema_version":"1.0","source":{"id":"1506.07201","kind":"arxiv","version":1}},"canonical_sha256":"3223a2eb9673614970c054f1897d79d002ea334c4e4cede646671c6db476fb62","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3223a2eb9673614970c054f1897d79d002ea334c4e4cede646671c6db476fb62","first_computed_at":"2026-05-17T23:49:53.440789Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:53.440789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0dX7FFA5NcIntwnnzEc3FnKjwFKihUKdeoZFoJs29q9ElYimOqSs/trgez2E+J8aWDOCwwvr5+2PD9XyeqA+BA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:53.441245Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.07201","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:79de98246cbd026406432f36538762c10f372ba11fca968f407e044ff1c3c906","sha256:d9a4f9658aba82d93a88e4d2d3c3c732428ca14282ed20621d61a78d42bf4b92"],"state_sha256":"ef56f01268fbd30e6fae567696b6c653254ce8d0acc9b9e858888a6f55d61e3a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"krNqE2BZ13RJ7zPLRm+rLTtQNhkw57U4etxHIW49XNf3cgtPRkGONM7qHAC4PMjdiBvLIfbmHWjC8Re72d8WDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T20:53:24.396141Z","bundle_sha256":"fe7e220ceae17b09e528f304e0ef7ac5062d2229e405a37a4a9452bd07ccbc68"}}