{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:4TVKD43JBLATPMIA5D27PNLIZK","short_pith_number":"pith:4TVKD43J","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"},"canonical_sha256":"e4eaa1f3690ac137b100e8f5f7b568ca974e3313c7773468ce8cfcc027777375","source":{"kind":"arxiv","id":"1512.04895","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.04895","created_at":"2026-05-18T00:34:39Z"},{"alias_kind":"arxiv_version","alias_value":"1512.04895v2","created_at":"2026-05-18T00:34:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.04895","created_at":"2026-05-18T00:34:39Z"},{"alias_kind":"pith_short_12","alias_value":"4TVKD43JBLAT","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4TVKD43JBLATPMIA","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4TVKD43J","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:4TVKD43JBLATPMIA5D27PNLIZK","target":"record","payload":{"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"},"canonical_sha256":"e4eaa1f3690ac137b100e8f5f7b568ca974e3313c7773468ce8cfcc027777375","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"},"source_kind":"arxiv","source_id":"1512.04895","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:34:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mdJBSlPDanm83c14hRzMXwAKr1qsb7AwHPIpPkMpIuYyLViK77YWydq6GJp8f00XztBUavMogjpfX98HKANrDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T01:33:18.562924Z"},"content_sha256":"ef778afa5b4c2c44f7a6eb60686064932fef2f4751f5ba6559937d83134f8d12","schema_version":"1.0","event_id":"sha256:ef778afa5b4c2c44f7a6eb60686064932fef2f4751f5ba6559937d83134f8d12"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:4TVKD43JBLATPMIA5D27PNLIZK","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:34:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TYN+2oEwBnTAWJTOsKgA3Tn9CsAe9r3+GaUfxBiz7KvJfSeAbuwpOdWA9jkRA7EyUKiC75PfxTXFxqXUFeL7Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T01:33:18.563268Z"},"content_sha256":"bc58fdca1ee056f4b016c9aa74d028fdfac9057f6fa58bd16a149b5b7fcf06c7","schema_version":"1.0","event_id":"sha256:bc58fdca1ee056f4b016c9aa74d028fdfac9057f6fa58bd16a149b5b7fcf06c7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4TVKD43JBLATPMIA5D27PNLIZK/bundle.json","state_url":"https://pith.science/pith/4TVKD43JBLATPMIA5D27PNLIZK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4TVKD43JBLATPMIA5D27PNLIZK/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":"2026-06-23T01:33:18Z","links":{"resolver":"https://pith.science/pith/4TVKD43JBLATPMIA5D27PNLIZK","bundle":"https://pith.science/pith/4TVKD43JBLATPMIA5D27PNLIZK/bundle.json","state":"https://pith.science/pith/4TVKD43JBLATPMIA5D27PNLIZK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4TVKD43JBLATPMIA5D27PNLIZK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:4TVKD43JBLATPMIA5D27PNLIZK","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":"46eb6566382902e58f73ab02fc2bdecdea5a3a41fd9a98e59a319fd7b5596593","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-12-15T18:51:17Z","title_canon_sha256":"ac434d49edf4e7570d44b67d52e64e0d37cbd008f19d3f335b948cf2df4f887f"},"schema_version":"1.0","source":{"id":"1512.04895","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.04895","created_at":"2026-05-18T00:34:39Z"},{"alias_kind":"arxiv_version","alias_value":"1512.04895v2","created_at":"2026-05-18T00:34:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.04895","created_at":"2026-05-18T00:34:39Z"},{"alias_kind":"pith_short_12","alias_value":"4TVKD43JBLAT","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4TVKD43JBLATPMIA","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4TVKD43J","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:bc58fdca1ee056f4b016c9aa74d028fdfac9057f6fa58bd16a149b5b7fcf06c7","target":"graph","created_at":"2026-05-18T00:34:39Z","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":"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","authors_text":"Sonia L'Innocente, Vincenzo Mantova","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-12-15T18:51:17Z","title":"Factorisation of germ-like series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04895","kind":"arxiv","version":2},"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:ef778afa5b4c2c44f7a6eb60686064932fef2f4751f5ba6559937d83134f8d12","target":"record","created_at":"2026-05-18T00:34:39Z","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":"46eb6566382902e58f73ab02fc2bdecdea5a3a41fd9a98e59a319fd7b5596593","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-12-15T18:51:17Z","title_canon_sha256":"ac434d49edf4e7570d44b67d52e64e0d37cbd008f19d3f335b948cf2df4f887f"},"schema_version":"1.0","source":{"id":"1512.04895","kind":"arxiv","version":2}},"canonical_sha256":"e4eaa1f3690ac137b100e8f5f7b568ca974e3313c7773468ce8cfcc027777375","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4eaa1f3690ac137b100e8f5f7b568ca974e3313c7773468ce8cfcc027777375","first_computed_at":"2026-05-18T00:34:39.512212Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:39.512212Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0tXnPOn3ClKL13p8uck39iXaNFAIaKjWjJkv4Oz4zv/SSN7VKHumc0BePTYQsKAG7PLsS7Dr0dwoCsoJXxt+Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:39.512729Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.04895","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef778afa5b4c2c44f7a6eb60686064932fef2f4751f5ba6559937d83134f8d12","sha256:bc58fdca1ee056f4b016c9aa74d028fdfac9057f6fa58bd16a149b5b7fcf06c7"],"state_sha256":"eb1595c73ddffe09e865b0f374e76ea04747a3ec9bc1e853610a35f51e59d7af"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9Q4CpoFbHjDFjIviLGJTFHXNSEeNFIKypyiKoe0WzVBUCGi6fCcirdpoT7xBJYgtD3xuhHc+eZ5Ibxrv6dV8Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T01:33:18.565739Z","bundle_sha256":"52a976caf00ace8b89b7e0b73ee774dcee4d07a7c1095c18b32f7ab74b4dc119"}}