{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:3V4S63VQTPVKAPZSR3ATGHRMYQ","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":"c4efb20a28e25486058946f44822527edb2dc29af2cdc85a65c9a0466a0b3b1d","cross_cats_sorted":["gr-qc","hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-11-07T16:34:48Z","title_canon_sha256":"d627fef2a9f5e8e923197373359f92abb072d193dd51379f97fa11a3d7c0dc71"},"schema_version":"1.0","source":{"id":"1811.02972","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.02972","created_at":"2026-05-18T00:01:20Z"},{"alias_kind":"arxiv_version","alias_value":"1811.02972v1","created_at":"2026-05-18T00:01:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.02972","created_at":"2026-05-18T00:01:20Z"},{"alias_kind":"pith_short_12","alias_value":"3V4S63VQTPVK","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"3V4S63VQTPVKAPZS","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"3V4S63VQ","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:8be2bc89fea3c36069a36b2f85ae290b655a13fa5dbf2abafa8ed641f95365e5","target":"graph","created_at":"2026-05-18T00:01:20Z","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":"We obtain an explicit formula for the full expansion of the spectral action on Robertson-Walker spacetimes, expressed in terms of Bell polynomials, using Brownian bridge integrals and the Feynman-Kac formula. We then apply this result to the case of multifractal Packed Swiss Cheese Cosmology models obtained from an arrangement of Robertson-Walker spacetimes along an Apollonian sphere packing. Using Mellin transforms, we show that the asymptotic expansion of the spectral action contains the same terms as in the case of a single Robertson-Walker spacetime, but with zeta-regularized coefficients,","authors_text":"Farzad Fathizadeh, Matilde Marcolli, Yeorgia Kafkoulis","cross_cats":["gr-qc","hep-th","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-11-07T16:34:48Z","title":"Bell polynomials and Brownian bridge in Spectral Gravity models on multifractal Robertson-Walker cosmologies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.02972","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:d4b8c154704bad6198a16c920ed56c5802c1429af4c34c06ded5380240d0bee5","target":"record","created_at":"2026-05-18T00:01:20Z","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":"c4efb20a28e25486058946f44822527edb2dc29af2cdc85a65c9a0466a0b3b1d","cross_cats_sorted":["gr-qc","hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-11-07T16:34:48Z","title_canon_sha256":"d627fef2a9f5e8e923197373359f92abb072d193dd51379f97fa11a3d7c0dc71"},"schema_version":"1.0","source":{"id":"1811.02972","kind":"arxiv","version":1}},"canonical_sha256":"dd792f6eb09beaa03f328ec1331e2cc42cdf9575a2275c8de31109350e99d0d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd792f6eb09beaa03f328ec1331e2cc42cdf9575a2275c8de31109350e99d0d4","first_computed_at":"2026-05-18T00:01:20.250477Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:20.250477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rOl6948pkWa9BIskaM/GvuQZsJLe1hXC5fWAhOvRJlr54IuE3T9DODitVsHiqQ78da43ygLYdH3ex3MpCzY0Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:20.250958Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.02972","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d4b8c154704bad6198a16c920ed56c5802c1429af4c34c06ded5380240d0bee5","sha256:8be2bc89fea3c36069a36b2f85ae290b655a13fa5dbf2abafa8ed641f95365e5"],"state_sha256":"e4bc485db180bc6fcecb39c578a86430892feaf7691ea2786155b21c2de4690f"}