{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:BBZ2OONXFFAA74XPRZNWO2VSCU","short_pith_number":"pith:BBZ2OONX","canonical_record":{"source":{"id":"2407.02580","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2024-07-02T18:02:21Z","cross_cats_sorted":["astro-ph.CO","gr-qc"],"title_canon_sha256":"1669da4d1da3783e90bb038a070d959a22317e7a94b319d41047c51653f55e0d","abstract_canon_sha256":"9073a0ccb1237bfabedf37950ba768a79f82f96cde2a6343dcc667329c1bede8"},"schema_version":"1.0"},"canonical_sha256":"0873a739b729400ff2ef8e5b676ab2151054acf4d58fad5f5cbce71d2b5ee8ef","source":{"kind":"arxiv","id":"2407.02580","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.02580","created_at":"2026-07-05T08:39:38Z"},{"alias_kind":"arxiv_version","alias_value":"2407.02580v1","created_at":"2026-07-05T08:39:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.02580","created_at":"2026-07-05T08:39:38Z"},{"alias_kind":"pith_short_12","alias_value":"BBZ2OONXFFAA","created_at":"2026-07-05T08:39:38Z"},{"alias_kind":"pith_short_16","alias_value":"BBZ2OONXFFAA74XP","created_at":"2026-07-05T08:39:38Z"},{"alias_kind":"pith_short_8","alias_value":"BBZ2OONX","created_at":"2026-07-05T08:39:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:BBZ2OONXFFAA74XPRZNWO2VSCU","target":"record","payload":{"canonical_record":{"source":{"id":"2407.02580","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2024-07-02T18:02:21Z","cross_cats_sorted":["astro-ph.CO","gr-qc"],"title_canon_sha256":"1669da4d1da3783e90bb038a070d959a22317e7a94b319d41047c51653f55e0d","abstract_canon_sha256":"9073a0ccb1237bfabedf37950ba768a79f82f96cde2a6343dcc667329c1bede8"},"schema_version":"1.0"},"canonical_sha256":"0873a739b729400ff2ef8e5b676ab2151054acf4d58fad5f5cbce71d2b5ee8ef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:39:38.624431Z","signature_b64":"s4w2+UbYzt5w3EqcRymHUkiCRgxs9G4yXcfcAX1hi/huu9uWZ+emKLlsNsOGBCVex8GMpEX5g8KKrU3npyb8Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0873a739b729400ff2ef8e5b676ab2151054acf4d58fad5f5cbce71d2b5ee8ef","last_reissued_at":"2026-07-05T08:39:38.623986Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:39:38.623986Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2407.02580","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":"2026-07-05T08:39:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xSzBypf+Hm8GgKjcRSNmSC6wga3BcEg3Mfx9BPt8apPbaQt7nW2SSZEYcRsUrvC4zaxidkHxpbmZamWeFUSTDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T10:07:27.484322Z"},"content_sha256":"b5b8cd3116042dbce4ca60d083400069e1455735c8ca0b4e3f71eff25937096e","schema_version":"1.0","event_id":"sha256:b5b8cd3116042dbce4ca60d083400069e1455735c8ca0b4e3f71eff25937096e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:BBZ2OONXFFAA74XPRZNWO2VSCU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Precise Fitting Formula for Gravitational Wave Spectra from Phase Transitions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["astro-ph.CO","gr-qc"],"primary_cat":"hep-ph","authors_text":"Fazlollah Hajkarim, Graham White, Huai-Ke Guo, Kuver Sinha, Yang Xiao","submitted_at":"2024-07-02T18:02:21Z","abstract_excerpt":"Obtaining a precise form for the predicted gravitational wave (GW) spectrum from a phase transition is a topic of great relevance for beyond Standard Model (BSM) physicists. Currently, the most sophisticated semi-analytic framework for estimating the dominant contribution to the spectrum is the sound shell model; however, full calculations within this framework can be computationally expensive, especially for large-scale scans. The community therefore generally manages with fit functions to the GW spectrum, the most widely used of which is a single broken power law. We provide a more precise f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.02580","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.02580/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":"2026-07-05T08:39:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LXzH10EiECoYVpynxG1kMxx+Q5dQjNVKs0wwC4SQ1WxyvcoaOjThUCtR0wGpPTzYesYbGFEjNHBAZaqFaFBMDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T10:07:27.484913Z"},"content_sha256":"842c6fafc326bd34b529c8b62531b2176e1d4b5eefe89e75d6b3582ec2c24cbc","schema_version":"1.0","event_id":"sha256:842c6fafc326bd34b529c8b62531b2176e1d4b5eefe89e75d6b3582ec2c24cbc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BBZ2OONXFFAA74XPRZNWO2VSCU/bundle.json","state_url":"https://pith.science/pith/BBZ2OONXFFAA74XPRZNWO2VSCU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BBZ2OONXFFAA74XPRZNWO2VSCU/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":"2026-08-11T10:07:27Z","links":{"resolver":"https://pith.science/pith/BBZ2OONXFFAA74XPRZNWO2VSCU","bundle":"https://pith.science/pith/BBZ2OONXFFAA74XPRZNWO2VSCU/bundle.json","state":"https://pith.science/pith/BBZ2OONXFFAA74XPRZNWO2VSCU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BBZ2OONXFFAA74XPRZNWO2VSCU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:BBZ2OONXFFAA74XPRZNWO2VSCU","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":"9073a0ccb1237bfabedf37950ba768a79f82f96cde2a6343dcc667329c1bede8","cross_cats_sorted":["astro-ph.CO","gr-qc"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2024-07-02T18:02:21Z","title_canon_sha256":"1669da4d1da3783e90bb038a070d959a22317e7a94b319d41047c51653f55e0d"},"schema_version":"1.0","source":{"id":"2407.02580","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.02580","created_at":"2026-07-05T08:39:38Z"},{"alias_kind":"arxiv_version","alias_value":"2407.02580v1","created_at":"2026-07-05T08:39:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.02580","created_at":"2026-07-05T08:39:38Z"},{"alias_kind":"pith_short_12","alias_value":"BBZ2OONXFFAA","created_at":"2026-07-05T08:39:38Z"},{"alias_kind":"pith_short_16","alias_value":"BBZ2OONXFFAA74XP","created_at":"2026-07-05T08:39:38Z"},{"alias_kind":"pith_short_8","alias_value":"BBZ2OONX","created_at":"2026-07-05T08:39:38Z"}],"graph_snapshots":[{"event_id":"sha256:842c6fafc326bd34b529c8b62531b2176e1d4b5eefe89e75d6b3582ec2c24cbc","target":"graph","created_at":"2026-07-05T08:39:38Z","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/2407.02580/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Obtaining a precise form for the predicted gravitational wave (GW) spectrum from a phase transition is a topic of great relevance for beyond Standard Model (BSM) physicists. Currently, the most sophisticated semi-analytic framework for estimating the dominant contribution to the spectrum is the sound shell model; however, full calculations within this framework can be computationally expensive, especially for large-scale scans. The community therefore generally manages with fit functions to the GW spectrum, the most widely used of which is a single broken power law. We provide a more precise f","authors_text":"Fazlollah Hajkarim, Graham White, Huai-Ke Guo, Kuver Sinha, Yang Xiao","cross_cats":["astro-ph.CO","gr-qc"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2024-07-02T18:02:21Z","title":"A Precise Fitting Formula for Gravitational Wave Spectra from Phase Transitions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.02580","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:b5b8cd3116042dbce4ca60d083400069e1455735c8ca0b4e3f71eff25937096e","target":"record","created_at":"2026-07-05T08:39:38Z","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":"9073a0ccb1237bfabedf37950ba768a79f82f96cde2a6343dcc667329c1bede8","cross_cats_sorted":["astro-ph.CO","gr-qc"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2024-07-02T18:02:21Z","title_canon_sha256":"1669da4d1da3783e90bb038a070d959a22317e7a94b319d41047c51653f55e0d"},"schema_version":"1.0","source":{"id":"2407.02580","kind":"arxiv","version":1}},"canonical_sha256":"0873a739b729400ff2ef8e5b676ab2151054acf4d58fad5f5cbce71d2b5ee8ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0873a739b729400ff2ef8e5b676ab2151054acf4d58fad5f5cbce71d2b5ee8ef","first_computed_at":"2026-07-05T08:39:38.623986Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:39:38.623986Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s4w2+UbYzt5w3EqcRymHUkiCRgxs9G4yXcfcAX1hi/huu9uWZ+emKLlsNsOGBCVex8GMpEX5g8KKrU3npyb8Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T08:39:38.624431Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.02580","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5b8cd3116042dbce4ca60d083400069e1455735c8ca0b4e3f71eff25937096e","sha256:842c6fafc326bd34b529c8b62531b2176e1d4b5eefe89e75d6b3582ec2c24cbc"],"state_sha256":"69b48ec7c49329986f07f1bcbe3b3a5d1121c02a13576f73eebab66768ec86ee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1B2OisR4uWVrxbd72E3BQXJlXK8EEbthl6OxV5n2O96e4AMf0SPTFiPr2RPbEp7C321ExObBw+GbZIwbv76mDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T10:07:27.488938Z","bundle_sha256":"b8c0a8c98db2ab14efea562b3ff285375a1edde16aca130aaecf07f65703226f"}}