{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:4ITQSCNF2GARFSZJOXEEQU2R5S","short_pith_number":"pith:4ITQSCNF","canonical_record":{"source":{"id":"2502.02661","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2025-02-04T19:02:42Z","cross_cats_sorted":[],"title_canon_sha256":"2a49fbe94daf02a5cdbc4bbcee3c3f306d11d4a51ee58359f5bcd05db729d752","abstract_canon_sha256":"1ce2b8a62659481f3be15569d99377fce1d972a10831bf36c183dff6f928c2df"},"schema_version":"1.0"},"canonical_sha256":"e2270909a5d18112cb2975c8485351ecbbde183ae5a28d9e8edd7d23d5daa6fc","source":{"kind":"arxiv","id":"2502.02661","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.02661","created_at":"2026-07-05T11:17:40Z"},{"alias_kind":"arxiv_version","alias_value":"2502.02661v2","created_at":"2026-07-05T11:17:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.02661","created_at":"2026-07-05T11:17:40Z"},{"alias_kind":"pith_short_12","alias_value":"4ITQSCNF2GAR","created_at":"2026-07-05T11:17:40Z"},{"alias_kind":"pith_short_16","alias_value":"4ITQSCNF2GARFSZJ","created_at":"2026-07-05T11:17:40Z"},{"alias_kind":"pith_short_8","alias_value":"4ITQSCNF","created_at":"2026-07-05T11:17:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:4ITQSCNF2GARFSZJOXEEQU2R5S","target":"record","payload":{"canonical_record":{"source":{"id":"2502.02661","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2025-02-04T19:02:42Z","cross_cats_sorted":[],"title_canon_sha256":"2a49fbe94daf02a5cdbc4bbcee3c3f306d11d4a51ee58359f5bcd05db729d752","abstract_canon_sha256":"1ce2b8a62659481f3be15569d99377fce1d972a10831bf36c183dff6f928c2df"},"schema_version":"1.0"},"canonical_sha256":"e2270909a5d18112cb2975c8485351ecbbde183ae5a28d9e8edd7d23d5daa6fc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:17:40.854604Z","signature_b64":"ape3Ja5UjDxDRpj71hqzo3ESUKomrk4LN1j6uh9PKUlbPTChiaUHNiI1Vr0E47FPy1LJwd/NinkTwMTXN2PRDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e2270909a5d18112cb2975c8485351ecbbde183ae5a28d9e8edd7d23d5daa6fc","last_reissued_at":"2026-07-05T11:17:40.854120Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:17:40.854120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.02661","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":"2026-07-05T11:17:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4zMMkewCsHhquKtjzKvByxXD/saG0Bqi80XesY2qBPGzhaTEOBmq3ND6zSCmB0u3Nj4mBNKaUclSZtnhHkNWDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T23:46:07.739221Z"},"content_sha256":"458f0e59061a80b71024c74be42fe52133ba1e604dd568901cfc811e9f7a0ebd","schema_version":"1.0","event_id":"sha256:458f0e59061a80b71024c74be42fe52133ba1e604dd568901cfc811e9f7a0ebd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:4ITQSCNF2GARFSZJOXEEQU2R5S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Conformal Primon Gas at the End of Time","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Ming Yang, Sean A. Hartnoll","submitted_at":"2025-02-04T19:02:42Z","abstract_excerpt":"The Belinksy-Khalatnikov-Lifshitz dynamics of gravity close to a spacelike singularity can be mapped, at each point in space separately, onto the motion of a particle bouncing within half the fundamental domain of the modular group. We show that the semiclassical quantisation of this motion is a conformal quantum mechanics where the states are constrained to be modular invariant. Each such state defines an odd automorphic $L$-function. In particular, in a basis of dilatation eigenstates the wavefunction is proportional to the $L$-function along the critical axis and hence vanishes at the nontr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.02661","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.02661/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":"2026-07-05T11:17:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JkzgBO4xa5Y+KxLlop60C+P4dmHn3eQlzKxs+rO2l3P/ruz/4psmHJBpYdKlYwYnuGb/p5up8KSD+tz2S57PBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T23:46:07.739693Z"},"content_sha256":"16988e4badc8cc5719ecfcef6d457b2b17f1f21ac5424f30b7f282471a9dc44d","schema_version":"1.0","event_id":"sha256:16988e4badc8cc5719ecfcef6d457b2b17f1f21ac5424f30b7f282471a9dc44d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4ITQSCNF2GARFSZJOXEEQU2R5S/bundle.json","state_url":"https://pith.science/pith/4ITQSCNF2GARFSZJOXEEQU2R5S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4ITQSCNF2GARFSZJOXEEQU2R5S/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":"2026-08-07T23:46:07Z","links":{"resolver":"https://pith.science/pith/4ITQSCNF2GARFSZJOXEEQU2R5S","bundle":"https://pith.science/pith/4ITQSCNF2GARFSZJOXEEQU2R5S/bundle.json","state":"https://pith.science/pith/4ITQSCNF2GARFSZJOXEEQU2R5S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4ITQSCNF2GARFSZJOXEEQU2R5S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:4ITQSCNF2GARFSZJOXEEQU2R5S","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":"1ce2b8a62659481f3be15569d99377fce1d972a10831bf36c183dff6f928c2df","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2025-02-04T19:02:42Z","title_canon_sha256":"2a49fbe94daf02a5cdbc4bbcee3c3f306d11d4a51ee58359f5bcd05db729d752"},"schema_version":"1.0","source":{"id":"2502.02661","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.02661","created_at":"2026-07-05T11:17:40Z"},{"alias_kind":"arxiv_version","alias_value":"2502.02661v2","created_at":"2026-07-05T11:17:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.02661","created_at":"2026-07-05T11:17:40Z"},{"alias_kind":"pith_short_12","alias_value":"4ITQSCNF2GAR","created_at":"2026-07-05T11:17:40Z"},{"alias_kind":"pith_short_16","alias_value":"4ITQSCNF2GARFSZJ","created_at":"2026-07-05T11:17:40Z"},{"alias_kind":"pith_short_8","alias_value":"4ITQSCNF","created_at":"2026-07-05T11:17:40Z"}],"graph_snapshots":[{"event_id":"sha256:16988e4badc8cc5719ecfcef6d457b2b17f1f21ac5424f30b7f282471a9dc44d","target":"graph","created_at":"2026-07-05T11:17:40Z","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/2502.02661/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Belinksy-Khalatnikov-Lifshitz dynamics of gravity close to a spacelike singularity can be mapped, at each point in space separately, onto the motion of a particle bouncing within half the fundamental domain of the modular group. We show that the semiclassical quantisation of this motion is a conformal quantum mechanics where the states are constrained to be modular invariant. Each such state defines an odd automorphic $L$-function. In particular, in a basis of dilatation eigenstates the wavefunction is proportional to the $L$-function along the critical axis and hence vanishes at the nontr","authors_text":"Ming Yang, Sean A. Hartnoll","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2025-02-04T19:02:42Z","title":"The Conformal Primon Gas at the End of Time"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.02661","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":"sha256:458f0e59061a80b71024c74be42fe52133ba1e604dd568901cfc811e9f7a0ebd","target":"record","created_at":"2026-07-05T11:17:40Z","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":"1ce2b8a62659481f3be15569d99377fce1d972a10831bf36c183dff6f928c2df","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2025-02-04T19:02:42Z","title_canon_sha256":"2a49fbe94daf02a5cdbc4bbcee3c3f306d11d4a51ee58359f5bcd05db729d752"},"schema_version":"1.0","source":{"id":"2502.02661","kind":"arxiv","version":2}},"canonical_sha256":"e2270909a5d18112cb2975c8485351ecbbde183ae5a28d9e8edd7d23d5daa6fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e2270909a5d18112cb2975c8485351ecbbde183ae5a28d9e8edd7d23d5daa6fc","first_computed_at":"2026-07-05T11:17:40.854120Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:17:40.854120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ape3Ja5UjDxDRpj71hqzo3ESUKomrk4LN1j6uh9PKUlbPTChiaUHNiI1Vr0E47FPy1LJwd/NinkTwMTXN2PRDw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:17:40.854604Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.02661","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:458f0e59061a80b71024c74be42fe52133ba1e604dd568901cfc811e9f7a0ebd","sha256:16988e4badc8cc5719ecfcef6d457b2b17f1f21ac5424f30b7f282471a9dc44d"],"state_sha256":"5bd835fa63cd1b1fcbf386bebd7db61dfe756543c1c0141bda08891484395d0a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2cqXWcVECtj5TIK8wpjQY1EUY8ndV9/ZWlQRIV3GOcEIUmJFLZonQcAzq80idZbSZ3e+8MZ+wWIh8nOsQJo8Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T23:46:07.743699Z","bundle_sha256":"0c90f518cdc5d8d526786372bc1ac2392c8130a4c6944e4b8c1fde2a0944bce2"}}