{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:SKTSOVJKLMDVIMDHBJNQ3FUJHW","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":"088a0d09c8e778faaeac31723bd5ee107c9517889678202ba9a29f2569f4bd3f","cross_cats_sorted":["gr-qc","hep-ph"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"astro-ph.CO","submitted_at":"2025-07-17T10:10:33Z","title_canon_sha256":"d9f3a71559a469abb265e6259824fab09c310ddf2011c514d5d492360f2c2494"},"schema_version":"1.0","source":{"id":"2507.12968","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.12968","created_at":"2026-07-05T11:38:42Z"},{"alias_kind":"arxiv_version","alias_value":"2507.12968v1","created_at":"2026-07-05T11:38:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.12968","created_at":"2026-07-05T11:38:42Z"},{"alias_kind":"pith_short_12","alias_value":"SKTSOVJKLMDV","created_at":"2026-07-05T11:38:42Z"},{"alias_kind":"pith_short_16","alias_value":"SKTSOVJKLMDVIMDH","created_at":"2026-07-05T11:38:42Z"},{"alias_kind":"pith_short_8","alias_value":"SKTSOVJK","created_at":"2026-07-05T11:38:42Z"}],"graph_snapshots":[{"event_id":"sha256:8a66d75d35227809b565cfa5d5dd139df4e035d8aa0d5c861978fa5a074d94db","target":"graph","created_at":"2026-07-05T11:38:42Z","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/2507.12968/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Bouncing cosmology offers a singularity-free alternative to inflation, but its minimal realization-comprising only four cosmic phases-predicts a simple power-law stochastic gravitational-wave background (SGWB) with a narrow observational window. We introduce the next-to-minimal bouncing cosmology (NMBC), which adds an extra early contraction phase that imprints a broken power-law feature in the SGWB spectrum, enhancing detectability. Using our matrix-representation method grounded in an inequality algebra, we derive a closed-form expression for the NMBC SGWB spectrum. From this analytical resu","authors_text":"Changhong Li","cross_cats":["gr-qc","hep-ph"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"astro-ph.CO","submitted_at":"2025-07-17T10:10:33Z","title":"Analytic Gravitational Wave Spectrum in Next-to-Minimal Bouncing Cosmology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.12968","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:e5170f41c2c7e06294049d978e2811cb38a75eb804421ddd88b50306dd04ffd1","target":"record","created_at":"2026-07-05T11:38:42Z","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":"088a0d09c8e778faaeac31723bd5ee107c9517889678202ba9a29f2569f4bd3f","cross_cats_sorted":["gr-qc","hep-ph"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"astro-ph.CO","submitted_at":"2025-07-17T10:10:33Z","title_canon_sha256":"d9f3a71559a469abb265e6259824fab09c310ddf2011c514d5d492360f2c2494"},"schema_version":"1.0","source":{"id":"2507.12968","kind":"arxiv","version":1}},"canonical_sha256":"92a727552a5b075430670a5b0d96893db0348b2d3fe47ecb51f1a1cd925e6fb9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"92a727552a5b075430670a5b0d96893db0348b2d3fe47ecb51f1a1cd925e6fb9","first_computed_at":"2026-07-05T11:38:42.360010Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:38:42.360010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DypnfsZyvOT/0LPpl6ScfADutroYh8mnju6knC50PwXW7sBAtIcow0UjI3zjbbGdfDZ3a9N/Da0o4Cswf/1SBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:38:42.360417Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.12968","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e5170f41c2c7e06294049d978e2811cb38a75eb804421ddd88b50306dd04ffd1","sha256:8a66d75d35227809b565cfa5d5dd139df4e035d8aa0d5c861978fa5a074d94db"],"state_sha256":"fa25721e80836bffef5901392457df2f007268f00a04fab174b3ab7cd61534ce"}