{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:4TVKD43JBLATPMIA5D27PNLIZK","short_pith_number":"pith:4TVKD43J","schema_version":"1.0","canonical_sha256":"e4eaa1f3690ac137b100e8f5f7b568ca974e3313c7773468ce8cfcc027777375","source":{"kind":"arxiv","id":"1512.04895","version":2},"attestation_state":"computed","paper":{"title":"Factorisation of germ-like series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Sonia L'Innocente, Vincenzo Mantova","submitted_at":"2015-12-15T18:51:17Z","abstract_excerpt":"A classical tool in the study of real closed fields are the fields $K((G))$ of generalised power series (i.e., formal sums with well-ordered support) with coefficients in a field $K$ of characteristic 0 and exponents in an ordered abelian group $G$. A fundamental result of Berarducci ensures the existence of irreducible series in the subring $K((G^{\\leq 0}))$ of $K((G))$ consisting of the generalised power series with non-positive exponents.\n  It is an open question whether the factorisations of a series in such subring have common refinements, and whether the factorisation becomes unique afte"},"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":"1512.04895","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-12-15T18:51:17Z","cross_cats_sorted":[],"title_canon_sha256":"ac434d49edf4e7570d44b67d52e64e0d37cbd008f19d3f335b948cf2df4f887f","abstract_canon_sha256":"46eb6566382902e58f73ab02fc2bdecdea5a3a41fd9a98e59a319fd7b5596593"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:39.512729Z","signature_b64":"0tXnPOn3ClKL13p8uck39iXaNFAIaKjWjJkv4Oz4zv/SSN7VKHumc0BePTYQsKAG7PLsS7Dr0dwoCsoJXxt+Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4eaa1f3690ac137b100e8f5f7b568ca974e3313c7773468ce8cfcc027777375","last_reissued_at":"2026-05-18T00:34:39.512212Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:39.512212Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Factorisation of germ-like series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Sonia L'Innocente, Vincenzo Mantova","submitted_at":"2015-12-15T18:51:17Z","abstract_excerpt":"A classical tool in the study of real closed fields are the fields $K((G))$ of generalised power series (i.e., formal sums with well-ordered support) with coefficients in a field $K$ of characteristic 0 and exponents in an ordered abelian group $G$. A fundamental result of Berarducci ensures the existence of irreducible series in the subring $K((G^{\\leq 0}))$ of $K((G))$ consisting of the generalised power series with non-positive exponents.\n  It is an open question whether the factorisations of a series in such subring have common refinements, and whether the factorisation becomes unique afte"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04895","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":""},"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":"1512.04895","created_at":"2026-05-18T00:34:39.512283+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.04895v2","created_at":"2026-05-18T00:34:39.512283+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.04895","created_at":"2026-05-18T00:34:39.512283+00:00"},{"alias_kind":"pith_short_12","alias_value":"4TVKD43JBLAT","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_16","alias_value":"4TVKD43JBLATPMIA","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_8","alias_value":"4TVKD43J","created_at":"2026-05-18T12:29:05.191682+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/4TVKD43JBLATPMIA5D27PNLIZK","json":"https://pith.science/pith/4TVKD43JBLATPMIA5D27PNLIZK.json","graph_json":"https://pith.science/api/pith-number/4TVKD43JBLATPMIA5D27PNLIZK/graph.json","events_json":"https://pith.science/api/pith-number/4TVKD43JBLATPMIA5D27PNLIZK/events.json","paper":"https://pith.science/paper/4TVKD43J"},"agent_actions":{"view_html":"https://pith.science/pith/4TVKD43JBLATPMIA5D27PNLIZK","download_json":"https://pith.science/pith/4TVKD43JBLATPMIA5D27PNLIZK.json","view_paper":"https://pith.science/paper/4TVKD43J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.04895&json=true","fetch_graph":"https://pith.science/api/pith-number/4TVKD43JBLATPMIA5D27PNLIZK/graph.json","fetch_events":"https://pith.science/api/pith-number/4TVKD43JBLATPMIA5D27PNLIZK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4TVKD43JBLATPMIA5D27PNLIZK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4TVKD43JBLATPMIA5D27PNLIZK/action/storage_attestation","attest_author":"https://pith.science/pith/4TVKD43JBLATPMIA5D27PNLIZK/action/author_attestation","sign_citation":"https://pith.science/pith/4TVKD43JBLATPMIA5D27PNLIZK/action/citation_signature","submit_replication":"https://pith.science/pith/4TVKD43JBLATPMIA5D27PNLIZK/action/replication_record"}},"created_at":"2026-05-18T00:34:39.512283+00:00","updated_at":"2026-05-18T00:34:39.512283+00:00"}