{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:V2BNJ5D5K5QUZ4V75ZI3OWWF5Y","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":"068387605e2144d85ca508c8b3a5314e4f19fcdd92357bcbbe46bc9284def7f8","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2013-11-28T03:12:22Z","title_canon_sha256":"2ece4123a1b3581559ed26ad99306193803388dbad41f838934b402b35aafb46"},"schema_version":"1.0","source":{"id":"1311.7192","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.7192","created_at":"2026-05-18T01:46:05Z"},{"alias_kind":"arxiv_version","alias_value":"1311.7192v1","created_at":"2026-05-18T01:46:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.7192","created_at":"2026-05-18T01:46:05Z"},{"alias_kind":"pith_short_12","alias_value":"V2BNJ5D5K5QU","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"V2BNJ5D5K5QUZ4V7","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"V2BNJ5D5","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:e286457a3896ffac3d5c6717c4c9afa13b5bcd70caf5a7bc67cb1f8d1f412490","target":"graph","created_at":"2026-05-18T01:46:05Z","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":"In the non-standard model of relic gravitational waves (RGWs) generated in the early universe, the theoretical spectrum of is mainly described by an amplitude $r$ and a spectral index $\\beta$, the latter usually being determined by the slope of the inflation potential. Pulsar timing arrays (PTAs) data have imposed constraints on the amplitude of strain spectrum for a power-law form as a phenomenological model. Applying these constraints to a generic, theoretical spectrum with $r$ and $\\beta$ as independent parameters, we convert the PTAs constraint into an upper bound on the index $\\beta$, whi","authors_text":"Cheng-Shi Zhao, Jin-Zhong Liu, Ming-lei Tong, Ting-Gao Yang, Wen Zhao, Yang Zhang","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2013-11-28T03:12:22Z","title":"Using pulsar timing arrays and the quantum normalization condition to constrain relic gravitational waves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7192","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":"sha256:05b41923a21fe619ef5d6a4f8f8857ef0ddf4f0827351edf06d1f8657036c91d","target":"record","created_at":"2026-05-18T01:46:05Z","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":"068387605e2144d85ca508c8b3a5314e4f19fcdd92357bcbbe46bc9284def7f8","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2013-11-28T03:12:22Z","title_canon_sha256":"2ece4123a1b3581559ed26ad99306193803388dbad41f838934b402b35aafb46"},"schema_version":"1.0","source":{"id":"1311.7192","kind":"arxiv","version":1}},"canonical_sha256":"ae82d4f47d57614cf2bfee51b75ac5ee2271231e254844a0907b28353e3802b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae82d4f47d57614cf2bfee51b75ac5ee2271231e254844a0907b28353e3802b9","first_computed_at":"2026-05-18T01:46:05.332159Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:46:05.332159Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jm8zlGq2Ke+G7wF529zleAnnIbxEBs4/vGLI1NNSjE3msRwK9JoeUFXgPLQZzd79zsKcrUAVpPgWTEtK4470Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:46:05.332822Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.7192","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05b41923a21fe619ef5d6a4f8f8857ef0ddf4f0827351edf06d1f8657036c91d","sha256:e286457a3896ffac3d5c6717c4c9afa13b5bcd70caf5a7bc67cb1f8d1f412490"],"state_sha256":"a70c82516ce8dfb92c06d3385d078d2b84cf091b76dbac1c338246eb63c1eb6c"}