{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:TEDW7FRTISTA45Y5S2NQGH5DCX","short_pith_number":"pith:TEDW7FRT","schema_version":"1.0","canonical_sha256":"99076f963344a60e771d969b031fa315f89f259bd75e4499ff5f541f416cabad","source":{"kind":"arxiv","id":"2605.22624","version":1},"attestation_state":"computed","paper":{"title":"On the self-similarity of rational power series with matrix coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.CO","authors_text":"Justin Vast, Pierre-Emmanuel Caprace","submitted_at":"2026-05-21T15:35:51Z","abstract_excerpt":"Let $p$ be a prime, let $d \\geq 1$ be an integer and $A$ be the algebra of square matrices of size $d$ over the field of order $p$. Let $P, Q \\in A[x_1, \\dots x_n]$ be polynomials in $n$ indeterminates with coefficients in $A$, such that $Q$ is invertible in $ A[\\![x_1, \\dots, x_n]\\!]$. Let also $\\mathcal M \\colon \\mathbf Z^n \\to A$ be the map associating to the $n$-tuple of integers $(\\alpha_1, \\dots, \\alpha_n)$ the coefficient of the monomial $x_1^{\\alpha_1} \\dots x_n^{\\alpha_n}$ in the development of the rational fraction $PQ^{-1}$ as a power series (the support of $\\mathcal M$ is contained"},"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":"2605.22624","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-21T15:35:51Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"8757cfe27bb3c7d8679edfd24fc5022645cbb81b90a0b562b97a773f1a2e3679","abstract_canon_sha256":"4dcf85ae0c7f628e481f53553fcb7b426124684adad50deffaf26e5d8936154a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-22T02:04:46.624844Z","signature_b64":"Ec591+hTAPSXcDSE8eRqYvM8AbQqasyOJso6qZgHyzd/NFwlIVvvU0yew85t1evE96bWmhKOdG1A9cO5PiJ7AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"99076f963344a60e771d969b031fa315f89f259bd75e4499ff5f541f416cabad","last_reissued_at":"2026-05-22T02:04:46.623928Z","signature_status":"signed_v1","first_computed_at":"2026-05-22T02:04:46.623928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the self-similarity of rational power series with matrix coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.CO","authors_text":"Justin Vast, Pierre-Emmanuel Caprace","submitted_at":"2026-05-21T15:35:51Z","abstract_excerpt":"Let $p$ be a prime, let $d \\geq 1$ be an integer and $A$ be the algebra of square matrices of size $d$ over the field of order $p$. Let $P, Q \\in A[x_1, \\dots x_n]$ be polynomials in $n$ indeterminates with coefficients in $A$, such that $Q$ is invertible in $ A[\\![x_1, \\dots, x_n]\\!]$. Let also $\\mathcal M \\colon \\mathbf Z^n \\to A$ be the map associating to the $n$-tuple of integers $(\\alpha_1, \\dots, \\alpha_n)$ the coefficient of the monomial $x_1^{\\alpha_1} \\dots x_n^{\\alpha_n}$ in the development of the rational fraction $PQ^{-1}$ as a power series (the support of $\\mathcal M$ is contained"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22624","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/2605.22624/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":"2605.22624","created_at":"2026-05-22T02:04:46.624084+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.22624v1","created_at":"2026-05-22T02:04:46.624084+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.22624","created_at":"2026-05-22T02:04:46.624084+00:00"},{"alias_kind":"pith_short_12","alias_value":"TEDW7FRTISTA","created_at":"2026-05-22T02:04:46.624084+00:00"},{"alias_kind":"pith_short_16","alias_value":"TEDW7FRTISTA45Y5","created_at":"2026-05-22T02:04:46.624084+00:00"},{"alias_kind":"pith_short_8","alias_value":"TEDW7FRT","created_at":"2026-05-22T02:04:46.624084+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TEDW7FRTISTA45Y5S2NQGH5DCX","json":"https://pith.science/pith/TEDW7FRTISTA45Y5S2NQGH5DCX.json","graph_json":"https://pith.science/api/pith-number/TEDW7FRTISTA45Y5S2NQGH5DCX/graph.json","events_json":"https://pith.science/api/pith-number/TEDW7FRTISTA45Y5S2NQGH5DCX/events.json","paper":"https://pith.science/paper/TEDW7FRT"},"agent_actions":{"view_html":"https://pith.science/pith/TEDW7FRTISTA45Y5S2NQGH5DCX","download_json":"https://pith.science/pith/TEDW7FRTISTA45Y5S2NQGH5DCX.json","view_paper":"https://pith.science/paper/TEDW7FRT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.22624&json=true","fetch_graph":"https://pith.science/api/pith-number/TEDW7FRTISTA45Y5S2NQGH5DCX/graph.json","fetch_events":"https://pith.science/api/pith-number/TEDW7FRTISTA45Y5S2NQGH5DCX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TEDW7FRTISTA45Y5S2NQGH5DCX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TEDW7FRTISTA45Y5S2NQGH5DCX/action/storage_attestation","attest_author":"https://pith.science/pith/TEDW7FRTISTA45Y5S2NQGH5DCX/action/author_attestation","sign_citation":"https://pith.science/pith/TEDW7FRTISTA45Y5S2NQGH5DCX/action/citation_signature","submit_replication":"https://pith.science/pith/TEDW7FRTISTA45Y5S2NQGH5DCX/action/replication_record"}},"created_at":"2026-05-22T02:04:46.624084+00:00","updated_at":"2026-05-22T02:04:46.624084+00:00"}