{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:EHWNCKLUEQY24O3LTN5E6ULAWZ","short_pith_number":"pith:EHWNCKLU","canonical_record":{"source":{"id":"2606.22431","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2026-06-21T10:44:26Z","cross_cats_sorted":["astro-ph.CO","hep-th"],"title_canon_sha256":"68433e627545be7fa557b860208b02273abc3261249ec5ec2a47403edfacf79e","abstract_canon_sha256":"4956169e288c957135d102bd483316b984e12872ff69086f2d36a562f6ea150f"},"schema_version":"1.0"},"canonical_sha256":"21ecd129742431ae3b6b9b7a4f5160b64e99bc33bb9a5926236d686ec357de7a","source":{"kind":"arxiv","id":"2606.22431","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.22431","created_at":"2026-06-23T02:13:38Z"},{"alias_kind":"arxiv_version","alias_value":"2606.22431v1","created_at":"2026-06-23T02:13:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.22431","created_at":"2026-06-23T02:13:38Z"},{"alias_kind":"pith_short_12","alias_value":"EHWNCKLUEQY2","created_at":"2026-06-23T02:13:38Z"},{"alias_kind":"pith_short_16","alias_value":"EHWNCKLUEQY24O3L","created_at":"2026-06-23T02:13:38Z"},{"alias_kind":"pith_short_8","alias_value":"EHWNCKLU","created_at":"2026-06-23T02:13:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:EHWNCKLUEQY24O3LTN5E6ULAWZ","target":"record","payload":{"canonical_record":{"source":{"id":"2606.22431","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2026-06-21T10:44:26Z","cross_cats_sorted":["astro-ph.CO","hep-th"],"title_canon_sha256":"68433e627545be7fa557b860208b02273abc3261249ec5ec2a47403edfacf79e","abstract_canon_sha256":"4956169e288c957135d102bd483316b984e12872ff69086f2d36a562f6ea150f"},"schema_version":"1.0"},"canonical_sha256":"21ecd129742431ae3b6b9b7a4f5160b64e99bc33bb9a5926236d686ec357de7a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T02:13:38.265957Z","signature_b64":"8I6aQlEqbJ7cZ9oEn6zR1hYZFJ6XEVtUXfvfJ/hFYSDECXYMALyZ9TJjEWThVUTgVqYvzOzg3zBvI5HSpyz1DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"21ecd129742431ae3b6b9b7a4f5160b64e99bc33bb9a5926236d686ec357de7a","last_reissued_at":"2026-06-23T02:13:38.265586Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T02:13:38.265586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.22431","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":"2026-06-23T02:13:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CuMp5YpSRgdpcJajfR501KBHdy7K2V7nMnqZspjDRFFeZm2rKmSZfJs3a2dUlSPARuLBeatzhrZVc8/s4k3oBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T09:39:05.686420Z"},"content_sha256":"f0345419cac6328181df9e849a7ff4d7f222e733f61464b9b5dacaf6666f430b","schema_version":"1.0","event_id":"sha256:f0345419cac6328181df9e849a7ff4d7f222e733f61464b9b5dacaf6666f430b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:EHWNCKLUEQY24O3LTN5E6ULAWZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Interplay Between Fractional Calculus and Holographic Dark Energy","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["astro-ph.CO","hep-th"],"primary_cat":"gr-qc","authors_text":"Ayush Bidlan","submitted_at":"2026-06-21T10:44:26Z","abstract_excerpt":"This dissertation aims to put forth a systematic construction of a fractional-calculus extension of holographic dark energy (HDE). We show that linking late-time cosmic acceleration to non-local or memory effects encoded in a fractional (Riesz) derivative within black hole thermodynamics produces deviations from standard HDE and can address some challenges of the Hubble cutoff. In particular, a Riesz fractional spatial derivative is introduced into the Hamiltonian constraint of a Schwarzschild black hole in quantum geometrodynamics, leading to a Fractional Wheeler--DeWitt equation whose soluti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22431","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/2606.22431/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":"2026-06-23T02:13:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dIZn7D7uDUZWPG8pEA0oVG3z0zyposUApVuvHJRdohyHgI7ZG0Me0h+x4RSugEEqthh1j9Z5f/B2I3Td8u6pBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T09:39:05.686893Z"},"content_sha256":"cd9ea9fab2f99c32a8aa6bcb3c8451feaf65aa0a6c2d57e1c5a34fa677b0f3ec","schema_version":"1.0","event_id":"sha256:cd9ea9fab2f99c32a8aa6bcb3c8451feaf65aa0a6c2d57e1c5a34fa677b0f3ec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EHWNCKLUEQY24O3LTN5E6ULAWZ/bundle.json","state_url":"https://pith.science/pith/EHWNCKLUEQY24O3LTN5E6ULAWZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EHWNCKLUEQY24O3LTN5E6ULAWZ/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":"2026-06-28T09:39:05Z","links":{"resolver":"https://pith.science/pith/EHWNCKLUEQY24O3LTN5E6ULAWZ","bundle":"https://pith.science/pith/EHWNCKLUEQY24O3LTN5E6ULAWZ/bundle.json","state":"https://pith.science/pith/EHWNCKLUEQY24O3LTN5E6ULAWZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EHWNCKLUEQY24O3LTN5E6ULAWZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:EHWNCKLUEQY24O3LTN5E6ULAWZ","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":"4956169e288c957135d102bd483316b984e12872ff69086f2d36a562f6ea150f","cross_cats_sorted":["astro-ph.CO","hep-th"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2026-06-21T10:44:26Z","title_canon_sha256":"68433e627545be7fa557b860208b02273abc3261249ec5ec2a47403edfacf79e"},"schema_version":"1.0","source":{"id":"2606.22431","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.22431","created_at":"2026-06-23T02:13:38Z"},{"alias_kind":"arxiv_version","alias_value":"2606.22431v1","created_at":"2026-06-23T02:13:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.22431","created_at":"2026-06-23T02:13:38Z"},{"alias_kind":"pith_short_12","alias_value":"EHWNCKLUEQY2","created_at":"2026-06-23T02:13:38Z"},{"alias_kind":"pith_short_16","alias_value":"EHWNCKLUEQY24O3L","created_at":"2026-06-23T02:13:38Z"},{"alias_kind":"pith_short_8","alias_value":"EHWNCKLU","created_at":"2026-06-23T02:13:38Z"}],"graph_snapshots":[{"event_id":"sha256:cd9ea9fab2f99c32a8aa6bcb3c8451feaf65aa0a6c2d57e1c5a34fa677b0f3ec","target":"graph","created_at":"2026-06-23T02:13:38Z","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/2606.22431/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This dissertation aims to put forth a systematic construction of a fractional-calculus extension of holographic dark energy (HDE). We show that linking late-time cosmic acceleration to non-local or memory effects encoded in a fractional (Riesz) derivative within black hole thermodynamics produces deviations from standard HDE and can address some challenges of the Hubble cutoff. In particular, a Riesz fractional spatial derivative is introduced into the Hamiltonian constraint of a Schwarzschild black hole in quantum geometrodynamics, leading to a Fractional Wheeler--DeWitt equation whose soluti","authors_text":"Ayush Bidlan","cross_cats":["astro-ph.CO","hep-th"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2026-06-21T10:44:26Z","title":"An Interplay Between Fractional Calculus and Holographic Dark Energy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22431","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:f0345419cac6328181df9e849a7ff4d7f222e733f61464b9b5dacaf6666f430b","target":"record","created_at":"2026-06-23T02:13:38Z","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":"4956169e288c957135d102bd483316b984e12872ff69086f2d36a562f6ea150f","cross_cats_sorted":["astro-ph.CO","hep-th"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2026-06-21T10:44:26Z","title_canon_sha256":"68433e627545be7fa557b860208b02273abc3261249ec5ec2a47403edfacf79e"},"schema_version":"1.0","source":{"id":"2606.22431","kind":"arxiv","version":1}},"canonical_sha256":"21ecd129742431ae3b6b9b7a4f5160b64e99bc33bb9a5926236d686ec357de7a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"21ecd129742431ae3b6b9b7a4f5160b64e99bc33bb9a5926236d686ec357de7a","first_computed_at":"2026-06-23T02:13:38.265586Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T02:13:38.265586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8I6aQlEqbJ7cZ9oEn6zR1hYZFJ6XEVtUXfvfJ/hFYSDECXYMALyZ9TJjEWThVUTgVqYvzOzg3zBvI5HSpyz1DQ==","signature_status":"signed_v1","signed_at":"2026-06-23T02:13:38.265957Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.22431","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f0345419cac6328181df9e849a7ff4d7f222e733f61464b9b5dacaf6666f430b","sha256:cd9ea9fab2f99c32a8aa6bcb3c8451feaf65aa0a6c2d57e1c5a34fa677b0f3ec"],"state_sha256":"0ffec95f083d8d43110684ab430ddc3ced8192cdf9b3fd09daba1385d7b5d8b8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"92D/J8rWpicQbcOZvxVmFPpworn/uvgeGanNjF57hZUwoLWIQ2ZtKquVcurHOrRuoU7MZ8J5CGvKvX6rRKpADQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T09:39:05.689166Z","bundle_sha256":"00ae5857b075eaf7c6072de81d43ea6478ad09272bbc2025b9d092cd2c7e4bfa"}}