{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:OU4I7ORTQ4FHLKAAUJQE4YWDRN","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":"f5458a0daed732f8f01e814228439f4083447f894bf93ec34189f78c2e91e853","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-05-09T09:13:23Z","title_canon_sha256":"2973c6a47892be04290bfb95008caa8e6a8c2e6e5792e4abd5ef14e53493f2e5"},"schema_version":"1.0","source":{"id":"1705.03240","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.03240","created_at":"2026-07-05T01:17:05Z"},{"alias_kind":"arxiv_version","alias_value":"1705.03240v2","created_at":"2026-07-05T01:17:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.03240","created_at":"2026-07-05T01:17:05Z"},{"alias_kind":"pith_short_12","alias_value":"OU4I7ORTQ4FH","created_at":"2026-07-05T01:17:05Z"},{"alias_kind":"pith_short_16","alias_value":"OU4I7ORTQ4FHLKAA","created_at":"2026-07-05T01:17:05Z"},{"alias_kind":"pith_short_8","alias_value":"OU4I7ORT","created_at":"2026-07-05T01:17:05Z"}],"graph_snapshots":[{"event_id":"sha256:0eebd58c4fa5a3a5d604cd81c67db0f0e11346e42860fe891a9834dc5010e865","target":"graph","created_at":"2026-07-05T01:17:05Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1705.03240/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the local invariants that a meromorphic $k$-differential on a Riemann surface of genus $g\\geq0$ can have. These local invariants are the orders of zeros and poles, and the $k$-residues at the poles. We show that for a given pattern of orders of zeroes, there exists, up to a few exceptions, a primitive $k$-differential having these orders of zero. The same is true for meromorphic $k$-differentials and in this case, we describe the tuples of complex numbers that can appear as $k$-residues at their poles. For genus $g\\geq2$, it turns out that every expected tuple appears as $k$-residues.","authors_text":"Guillaume Tahar, Quentin Gendron","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-05-09T09:13:23Z","title":"Diff\\'erentielles \\`a singularit\\'es prescrites"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03240","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:da31ae5d57cd53b2073548089d1731f75ca263e10492dca159a2140cad82c62d","target":"record","created_at":"2026-07-05T01:17:05Z","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":"f5458a0daed732f8f01e814228439f4083447f894bf93ec34189f78c2e91e853","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-05-09T09:13:23Z","title_canon_sha256":"2973c6a47892be04290bfb95008caa8e6a8c2e6e5792e4abd5ef14e53493f2e5"},"schema_version":"1.0","source":{"id":"1705.03240","kind":"arxiv","version":2}},"canonical_sha256":"75388fba33870a75a800a2604e62c38b610c15f2275c098c4b2c797b4f35a38e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"75388fba33870a75a800a2604e62c38b610c15f2275c098c4b2c797b4f35a38e","first_computed_at":"2026-07-05T01:17:05.380837Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:17:05.380837Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"81ITSRDVfMZqtDNMsblb3GLzxxzmCjKqeIHWF7yzzjTbL5Todboup385cSCD+kHCrSxAgUSitMIePZKAtGvSDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:17:05.381307Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.03240","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:da31ae5d57cd53b2073548089d1731f75ca263e10492dca159a2140cad82c62d","sha256:0eebd58c4fa5a3a5d604cd81c67db0f0e11346e42860fe891a9834dc5010e865"],"state_sha256":"c228e3212cfa4776d567a06b8d43a7b753efa637d6834a18afb449329f6ace38"}