{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:DP4CATEH5ZBVOLQN5MJUCMTRU6","short_pith_number":"pith:DP4CATEH","schema_version":"1.0","canonical_sha256":"1bf8204c87ee43572e0deb13413271a78d1cf14a4be8f632a8c967d8b995b932","source":{"kind":"arxiv","id":"2201.12316","version":2},"attestation_state":"computed","paper":{"title":"(Hurwitz-)Brill-Noether general marked graphs via the Demazure product","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CO","authors_text":"Nathan Pflueger","submitted_at":"2022-01-28T18:30:18Z","abstract_excerpt":"This paper gives a novel and compact proof that a metric graph consisting of a chain of loops of torsion order $0$ is Brill-Noether general (a theorem of Cools-Draisma-Payne-Robeva), and a finite or metric graph consisting of a chain of loops of torsion order $k$ is Hurwitz-Brill-Noether general in the sense of splitting loci (a theorem of Cook-Powell-Jensen). In fact, we prove a generalization to (metric) graphs with two marked points, that behaves well under vertex gluing. The key construction is a way to associate permutations to divisors on twice-marked graphs, simultaneously encoding the "},"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":"2201.12316","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-01-28T18:30:18Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"1c78ade77b7b967728378f1144c562d843f1856a1245f9774e3380ccffcdf804","abstract_canon_sha256":"3b0c497993fe48560b1ce3b66db509e8108d37c14843837538808b2dfe4dd351"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:01:09.665918Z","signature_b64":"dX+sHOCBJmMjykfSGxbI/Hl/VHVpcd3SyE4AiYaauaQGEz/5GVlcc9lZMYkU//3G0PmVRY1GrP4FXh9HyW43Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1bf8204c87ee43572e0deb13413271a78d1cf14a4be8f632a8c967d8b995b932","last_reissued_at":"2026-07-05T04:01:09.665502Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:01:09.665502Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"(Hurwitz-)Brill-Noether general marked graphs via the Demazure product","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CO","authors_text":"Nathan Pflueger","submitted_at":"2022-01-28T18:30:18Z","abstract_excerpt":"This paper gives a novel and compact proof that a metric graph consisting of a chain of loops of torsion order $0$ is Brill-Noether general (a theorem of Cools-Draisma-Payne-Robeva), and a finite or metric graph consisting of a chain of loops of torsion order $k$ is Hurwitz-Brill-Noether general in the sense of splitting loci (a theorem of Cook-Powell-Jensen). In fact, we prove a generalization to (metric) graphs with two marked points, that behaves well under vertex gluing. The key construction is a way to associate permutations to divisors on twice-marked graphs, simultaneously encoding the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.12316","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/2201.12316/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":"2201.12316","created_at":"2026-07-05T04:01:09.665558+00:00"},{"alias_kind":"arxiv_version","alias_value":"2201.12316v2","created_at":"2026-07-05T04:01:09.665558+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.12316","created_at":"2026-07-05T04:01:09.665558+00:00"},{"alias_kind":"pith_short_12","alias_value":"DP4CATEH5ZBV","created_at":"2026-07-05T04:01:09.665558+00:00"},{"alias_kind":"pith_short_16","alias_value":"DP4CATEH5ZBVOLQN","created_at":"2026-07-05T04:01:09.665558+00:00"},{"alias_kind":"pith_short_8","alias_value":"DP4CATEH","created_at":"2026-07-05T04:01:09.665558+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.03895","citing_title":"Transmission permutations and Demazure products in Hurwitz--Brill--Noether theory","ref_index":28,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DP4CATEH5ZBVOLQN5MJUCMTRU6","json":"https://pith.science/pith/DP4CATEH5ZBVOLQN5MJUCMTRU6.json","graph_json":"https://pith.science/api/pith-number/DP4CATEH5ZBVOLQN5MJUCMTRU6/graph.json","events_json":"https://pith.science/api/pith-number/DP4CATEH5ZBVOLQN5MJUCMTRU6/events.json","paper":"https://pith.science/paper/DP4CATEH"},"agent_actions":{"view_html":"https://pith.science/pith/DP4CATEH5ZBVOLQN5MJUCMTRU6","download_json":"https://pith.science/pith/DP4CATEH5ZBVOLQN5MJUCMTRU6.json","view_paper":"https://pith.science/paper/DP4CATEH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2201.12316&json=true","fetch_graph":"https://pith.science/api/pith-number/DP4CATEH5ZBVOLQN5MJUCMTRU6/graph.json","fetch_events":"https://pith.science/api/pith-number/DP4CATEH5ZBVOLQN5MJUCMTRU6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DP4CATEH5ZBVOLQN5MJUCMTRU6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DP4CATEH5ZBVOLQN5MJUCMTRU6/action/storage_attestation","attest_author":"https://pith.science/pith/DP4CATEH5ZBVOLQN5MJUCMTRU6/action/author_attestation","sign_citation":"https://pith.science/pith/DP4CATEH5ZBVOLQN5MJUCMTRU6/action/citation_signature","submit_replication":"https://pith.science/pith/DP4CATEH5ZBVOLQN5MJUCMTRU6/action/replication_record"}},"created_at":"2026-07-05T04:01:09.665558+00:00","updated_at":"2026-07-05T04:01:09.665558+00:00"}