{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:TXEOHL4XTDQCCOSQUIX24ENG3G","short_pith_number":"pith:TXEOHL4X","canonical_record":{"source":{"id":"1810.03565","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-08T16:32:29Z","cross_cats_sorted":[],"title_canon_sha256":"3c42e3ccb5c970826bdaac0e05796900b185688020721467b1df8e939ceddb4a","abstract_canon_sha256":"5f3d9a6ad9dbfc46bcebdd56e80da638d4d1dc231f58df4cc3050050e870c49d"},"schema_version":"1.0"},"canonical_sha256":"9dc8e3af9798e0213a50a22fae11a6d9874de48c47fdbe588fbe41eb91ccbc06","source":{"kind":"arxiv","id":"1810.03565","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.03565","created_at":"2026-05-18T00:03:50Z"},{"alias_kind":"arxiv_version","alias_value":"1810.03565v1","created_at":"2026-05-18T00:03:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.03565","created_at":"2026-05-18T00:03:50Z"},{"alias_kind":"pith_short_12","alias_value":"TXEOHL4XTDQC","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"TXEOHL4XTDQCCOSQ","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"TXEOHL4X","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:TXEOHL4XTDQCCOSQUIX24ENG3G","target":"record","payload":{"canonical_record":{"source":{"id":"1810.03565","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-08T16:32:29Z","cross_cats_sorted":[],"title_canon_sha256":"3c42e3ccb5c970826bdaac0e05796900b185688020721467b1df8e939ceddb4a","abstract_canon_sha256":"5f3d9a6ad9dbfc46bcebdd56e80da638d4d1dc231f58df4cc3050050e870c49d"},"schema_version":"1.0"},"canonical_sha256":"9dc8e3af9798e0213a50a22fae11a6d9874de48c47fdbe588fbe41eb91ccbc06","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:50.895862Z","signature_b64":"woDe1+KLF7UJFd+XOwY8ojzZTevOnLzceBOaYHcDOscInrdhu365orwU7AucxVWjuRvNIOj93y8/XRw4WhvbBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9dc8e3af9798e0213a50a22fae11a6d9874de48c47fdbe588fbe41eb91ccbc06","last_reissued_at":"2026-05-18T00:03:50.895174Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:50.895174Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.03565","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:03:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rqGSD+Fhb6RJMfp2LWyLfcLvBLb4uxe9AqImrp5mrLfItxz5t1vL2eZ9W6l2tWpQEj1qQMLySNx7RfzY7nI5Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T16:49:59.168987Z"},"content_sha256":"bcfae6be8e3d286438f30c7a2e612ca72015fecf5d10094bcc51bd115e7b47f1","schema_version":"1.0","event_id":"sha256:bcfae6be8e3d286438f30c7a2e612ca72015fecf5d10094bcc51bd115e7b47f1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:TXEOHL4XTDQCCOSQUIX24ENG3G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bi-pruned Hurwitz numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Marvin Anas Hahn","submitted_at":"2018-10-08T16:32:29Z","abstract_excerpt":"Hurwitz numbers enumerate ramified coverings of the Riemann sphere with fixed ramification data. Certain kinds of ramification data are of particular interest, such as double Hurwitz numbers, which count covers with fixed arbitrary ramification over $0$ and $\\infty$ and simple ramification over $b$ points, where $b$ is given by the Riemann-Hurwitz formula. In this work, we introduce the notion of bi-pruned double Hurwitz numbers. This is a new enumerative problem, which yields smaller numbers but completely determines double Hurwitz numbers. They count a relevant subset of covers and share man"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.03565","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":""},"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":"2026-05-18T00:03:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q8PsFhtpL5UU41p0p71IhnMSlmu5UtwyFh/wQU90IeHyg3cymXKV2TpyKCHtdIQ/s6QMSevQ3GHLXj34CACuAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T16:49:59.169345Z"},"content_sha256":"c8e34827a04bb400cdb82947a02aa9304713c35b7a8e769d6974ee9a965b21e1","schema_version":"1.0","event_id":"sha256:c8e34827a04bb400cdb82947a02aa9304713c35b7a8e769d6974ee9a965b21e1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TXEOHL4XTDQCCOSQUIX24ENG3G/bundle.json","state_url":"https://pith.science/pith/TXEOHL4XTDQCCOSQUIX24ENG3G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TXEOHL4XTDQCCOSQUIX24ENG3G/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":"2026-06-02T16:49:59Z","links":{"resolver":"https://pith.science/pith/TXEOHL4XTDQCCOSQUIX24ENG3G","bundle":"https://pith.science/pith/TXEOHL4XTDQCCOSQUIX24ENG3G/bundle.json","state":"https://pith.science/pith/TXEOHL4XTDQCCOSQUIX24ENG3G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TXEOHL4XTDQCCOSQUIX24ENG3G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:TXEOHL4XTDQCCOSQUIX24ENG3G","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":"5f3d9a6ad9dbfc46bcebdd56e80da638d4d1dc231f58df4cc3050050e870c49d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-08T16:32:29Z","title_canon_sha256":"3c42e3ccb5c970826bdaac0e05796900b185688020721467b1df8e939ceddb4a"},"schema_version":"1.0","source":{"id":"1810.03565","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.03565","created_at":"2026-05-18T00:03:50Z"},{"alias_kind":"arxiv_version","alias_value":"1810.03565v1","created_at":"2026-05-18T00:03:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.03565","created_at":"2026-05-18T00:03:50Z"},{"alias_kind":"pith_short_12","alias_value":"TXEOHL4XTDQC","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"TXEOHL4XTDQCCOSQ","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"TXEOHL4X","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:c8e34827a04bb400cdb82947a02aa9304713c35b7a8e769d6974ee9a965b21e1","target":"graph","created_at":"2026-05-18T00:03:50Z","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":"Hurwitz numbers enumerate ramified coverings of the Riemann sphere with fixed ramification data. Certain kinds of ramification data are of particular interest, such as double Hurwitz numbers, which count covers with fixed arbitrary ramification over $0$ and $\\infty$ and simple ramification over $b$ points, where $b$ is given by the Riemann-Hurwitz formula. In this work, we introduce the notion of bi-pruned double Hurwitz numbers. This is a new enumerative problem, which yields smaller numbers but completely determines double Hurwitz numbers. They count a relevant subset of covers and share man","authors_text":"Marvin Anas Hahn","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-08T16:32:29Z","title":"Bi-pruned Hurwitz numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.03565","kind":"arxiv","version":1},"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:bcfae6be8e3d286438f30c7a2e612ca72015fecf5d10094bcc51bd115e7b47f1","target":"record","created_at":"2026-05-18T00:03:50Z","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":"5f3d9a6ad9dbfc46bcebdd56e80da638d4d1dc231f58df4cc3050050e870c49d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-08T16:32:29Z","title_canon_sha256":"3c42e3ccb5c970826bdaac0e05796900b185688020721467b1df8e939ceddb4a"},"schema_version":"1.0","source":{"id":"1810.03565","kind":"arxiv","version":1}},"canonical_sha256":"9dc8e3af9798e0213a50a22fae11a6d9874de48c47fdbe588fbe41eb91ccbc06","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9dc8e3af9798e0213a50a22fae11a6d9874de48c47fdbe588fbe41eb91ccbc06","first_computed_at":"2026-05-18T00:03:50.895174Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:50.895174Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"woDe1+KLF7UJFd+XOwY8ojzZTevOnLzceBOaYHcDOscInrdhu365orwU7AucxVWjuRvNIOj93y8/XRw4WhvbBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:50.895862Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.03565","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bcfae6be8e3d286438f30c7a2e612ca72015fecf5d10094bcc51bd115e7b47f1","sha256:c8e34827a04bb400cdb82947a02aa9304713c35b7a8e769d6974ee9a965b21e1"],"state_sha256":"50438e9b5e91afb5fb6835c682680419302d52911791c1cb925f93bdf6cdd67c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sh6N4zMYAuOZAb7VDKBMsbPBAbMWcao86Yjix4FW/pvPseQbBdqbRDxMni6U8BpGg+dPIsBjeh8w5FR8HdzaCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T16:49:59.171269Z","bundle_sha256":"a2f9a349b3b2db30b2d29bf95e3781c0696062b3e8e0842a765a81582a58c88b"}}