{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:ZUGR3WNXZWYJNYUGI7IKMSYHS3","short_pith_number":"pith:ZUGR3WNX","schema_version":"1.0","canonical_sha256":"cd0d1dd9b7cdb096e28647d0a64b0796c6fdb172b2ecfd6eacbbcfda4f1f57fb","source":{"kind":"arxiv","id":"2512.14859","version":2},"attestation_state":"computed","paper":{"title":"Cosmology meets cluster algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Alessandro Palazio, Livia Ferro, Mattia Capuano, Tomasz Lukowski","submitted_at":"2025-12-16T19:21:44Z","abstract_excerpt":"In this paper we explore the mathematical properties of wavefunction coefficients in power-law FRW cosmologies, and establish their relation to cluster algebras. We focus on the particular contributions to the wavefunction coefficient coming from the path Feynman graphs, and show that the singularities of the wavefunction associated with a $n$-site path graph are related to the $\\mathcal{X}$-coordinates of the cluster algebra $A_{2n-2}$. To establish this relation, we consider the symbol of the de Sitter wavefunction coefficients and show that the letters appearing there are the region variabl"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2512.14859","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-12-16T19:21:44Z","cross_cats_sorted":[],"title_canon_sha256":"b62cc65ba7c7056b2105a8f423c4649e8a3995bbf5b2827f35bf246866a2b5e2","abstract_canon_sha256":"578f5744db066e08f0ba83afce41e5367b588aba886e191d9f28bfdc7b0b055f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-13T01:24:47.854966Z","signature_b64":"lqbQwqEpr8Zi4MfblpdI8w9q4cEF1Q+TzQcA4cK8zwPTWgGd8xEDoF4WUKzLYVPwIBiyWupVgNaSBUKsfQU/AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cd0d1dd9b7cdb096e28647d0a64b0796c6fdb172b2ecfd6eacbbcfda4f1f57fb","last_reissued_at":"2026-08-13T01:24:47.852644Z","signature_status":"signed_v1","first_computed_at":"2026-08-13T01:24:47.852644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cosmology meets cluster algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Alessandro Palazio, Livia Ferro, Mattia Capuano, Tomasz Lukowski","submitted_at":"2025-12-16T19:21:44Z","abstract_excerpt":"In this paper we explore the mathematical properties of wavefunction coefficients in power-law FRW cosmologies, and establish their relation to cluster algebras. We focus on the particular contributions to the wavefunction coefficient coming from the path Feynman graphs, and show that the singularities of the wavefunction associated with a $n$-site path graph are related to the $\\mathcal{X}$-coordinates of the cluster algebra $A_{2n-2}$. To establish this relation, we consider the symbol of the de Sitter wavefunction coefficients and show that the letters appearing there are the region variabl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.14859","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/2512.14859/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2512.14859","created_at":"2026-08-13T01:24:47.853764+00:00"},{"alias_kind":"arxiv_version","alias_value":"2512.14859v2","created_at":"2026-08-13T01:24:47.853764+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.14859","created_at":"2026-08-13T01:24:47.853764+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZUGR3WNXZWYJ","created_at":"2026-08-13T01:24:47.853764+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZUGR3WNXZWYJNYUG","created_at":"2026-08-13T01:24:47.853764+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZUGR3WNX","created_at":"2026-08-13T01:24:47.853764+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":4,"internal_anchor_count":4,"sample":[{"citing_arxiv_id":"2605.30797","citing_title":"A Boolean-Lattice Perspective for All-Loop Two-Site Cosmological Wavefunction","ref_index":17,"is_internal_anchor":true},{"citing_arxiv_id":"2604.26421","citing_title":"On the simplicity of de Sitter correlators","ref_index":47,"is_internal_anchor":true},{"citing_arxiv_id":"2605.06542","citing_title":"de Sitter Wavefunction from Quadrangular Polylogarithms: Chain Graphs","ref_index":23,"is_internal_anchor":true},{"citing_arxiv_id":"2604.22918","citing_title":"Kinematic Flow for Banana Loops and Unparticles","ref_index":61,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZUGR3WNXZWYJNYUGI7IKMSYHS3","json":"https://pith.science/pith/ZUGR3WNXZWYJNYUGI7IKMSYHS3.json","graph_json":"https://pith.science/api/pith-number/ZUGR3WNXZWYJNYUGI7IKMSYHS3/graph.json","events_json":"https://pith.science/api/pith-number/ZUGR3WNXZWYJNYUGI7IKMSYHS3/events.json","paper":"https://pith.science/paper/ZUGR3WNX"},"agent_actions":{"view_html":"https://pith.science/pith/ZUGR3WNXZWYJNYUGI7IKMSYHS3","download_json":"https://pith.science/pith/ZUGR3WNXZWYJNYUGI7IKMSYHS3.json","view_paper":"https://pith.science/paper/ZUGR3WNX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2512.14859&json=true","fetch_graph":"https://pith.science/api/pith-number/ZUGR3WNXZWYJNYUGI7IKMSYHS3/graph.json","fetch_events":"https://pith.science/api/pith-number/ZUGR3WNXZWYJNYUGI7IKMSYHS3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZUGR3WNXZWYJNYUGI7IKMSYHS3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZUGR3WNXZWYJNYUGI7IKMSYHS3/action/storage_attestation","attest_author":"https://pith.science/pith/ZUGR3WNXZWYJNYUGI7IKMSYHS3/action/author_attestation","sign_citation":"https://pith.science/pith/ZUGR3WNXZWYJNYUGI7IKMSYHS3/action/citation_signature","submit_replication":"https://pith.science/pith/ZUGR3WNXZWYJNYUGI7IKMSYHS3/action/replication_record"}},"created_at":"2026-08-13T01:24:47.853764+00:00","updated_at":"2026-08-13T01:24:47.853764+00:00"}