{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:D2MFIPWW6AHDLXKBHCF6WCBO2A","short_pith_number":"pith:D2MFIPWW","canonical_record":{"source":{"id":"1512.01598","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-12-05T00:20:48Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"1d163df063ad487f4f55f803d479a99d768d250fa3ca533e64d8041484ff62e8","abstract_canon_sha256":"c126f8eec1208f95aff0aceacabcc1fb416ff522ed4b7f3b1d4c947f3304ccf2"},"schema_version":"1.0"},"canonical_sha256":"1e98543ed6f00e35dd41388beb082ed01913d8896447167792370e7a9b2d2ee7","source":{"kind":"arxiv","id":"1512.01598","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.01598","created_at":"2026-05-18T00:11:11Z"},{"alias_kind":"arxiv_version","alias_value":"1512.01598v2","created_at":"2026-05-18T00:11:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.01598","created_at":"2026-05-18T00:11:11Z"},{"alias_kind":"pith_short_12","alias_value":"D2MFIPWW6AHD","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"D2MFIPWW6AHDLXKB","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"D2MFIPWW","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:D2MFIPWW6AHDLXKBHCF6WCBO2A","target":"record","payload":{"canonical_record":{"source":{"id":"1512.01598","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-12-05T00:20:48Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"1d163df063ad487f4f55f803d479a99d768d250fa3ca533e64d8041484ff62e8","abstract_canon_sha256":"c126f8eec1208f95aff0aceacabcc1fb416ff522ed4b7f3b1d4c947f3304ccf2"},"schema_version":"1.0"},"canonical_sha256":"1e98543ed6f00e35dd41388beb082ed01913d8896447167792370e7a9b2d2ee7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:11.945338Z","signature_b64":"9DpQbPvw1/OOIZFxBO2CXTdxz4e1V/UbkS1TB5CqheFxw3bubHTg+VL0hIgyTomucBpGSjM9UzzIFD7cBVEVAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1e98543ed6f00e35dd41388beb082ed01913d8896447167792370e7a9b2d2ee7","last_reissued_at":"2026-05-18T00:11:11.944632Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:11.944632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.01598","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":"2026-05-18T00:11:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G4CxG+F+5+PzFNjpuzAHDYH2TYZWgTL0yyL4MEAAu/+jqycUlFLUMvvA8cIooqI5j/MAzz5Cw8qcknGG0VEUDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T13:03:01.982716Z"},"content_sha256":"44d9b70cf3041d150f4a5e2ac2f2232ac4a60adafedbbf5789a3aa066440d4d4","schema_version":"1.0","event_id":"sha256:44d9b70cf3041d150f4a5e2ac2f2232ac4a60adafedbbf5789a3aa066440d4d4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:D2MFIPWW6AHDLXKBHCF6WCBO2A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pruned double Hurwitz numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CO","authors_text":"Marvin Anas Hahn","submitted_at":"2015-12-05T00:20:48Z","abstract_excerpt":"Hurwitz numbers count ramified genus $g$, degree $d$ coverings of the projective line with with fixed branch locus and fixed ramification data. Double Hurwitz numbers count such covers, where we fix two special profiles over $0$ and $\\infty$ and only simple ramification else. These objects feature insteresting structural behaviour and connections to geometry. In this paper, we introduce the notion of pruned double Hurwitz numbers, generalizing the notion of pruned simple Hurwitz numbers in \\cite{DN13}. We show that pruned double Hurwitz numbers, similar to usual double Hurwitz numbers, satisfy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01598","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":"2026-05-18T00:11:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KOxVDW+5150vpDVCC8Tsc+fnlO6sQp5k++MyUACFmBddEngp4xbsDe+WdiEDVp+hsh8h8UqyUPPY1eMRWEGoAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T13:03:01.983062Z"},"content_sha256":"44abb7a322c2843d66bd20380d300c5d74fdeaad55ae5f0e71e0744a13a871fe","schema_version":"1.0","event_id":"sha256:44abb7a322c2843d66bd20380d300c5d74fdeaad55ae5f0e71e0744a13a871fe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D2MFIPWW6AHDLXKBHCF6WCBO2A/bundle.json","state_url":"https://pith.science/pith/D2MFIPWW6AHDLXKBHCF6WCBO2A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D2MFIPWW6AHDLXKBHCF6WCBO2A/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":"2026-06-02T13:03:01Z","links":{"resolver":"https://pith.science/pith/D2MFIPWW6AHDLXKBHCF6WCBO2A","bundle":"https://pith.science/pith/D2MFIPWW6AHDLXKBHCF6WCBO2A/bundle.json","state":"https://pith.science/pith/D2MFIPWW6AHDLXKBHCF6WCBO2A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D2MFIPWW6AHDLXKBHCF6WCBO2A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:D2MFIPWW6AHDLXKBHCF6WCBO2A","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":"c126f8eec1208f95aff0aceacabcc1fb416ff522ed4b7f3b1d4c947f3304ccf2","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-12-05T00:20:48Z","title_canon_sha256":"1d163df063ad487f4f55f803d479a99d768d250fa3ca533e64d8041484ff62e8"},"schema_version":"1.0","source":{"id":"1512.01598","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.01598","created_at":"2026-05-18T00:11:11Z"},{"alias_kind":"arxiv_version","alias_value":"1512.01598v2","created_at":"2026-05-18T00:11:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.01598","created_at":"2026-05-18T00:11:11Z"},{"alias_kind":"pith_short_12","alias_value":"D2MFIPWW6AHD","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"D2MFIPWW6AHDLXKB","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"D2MFIPWW","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:44abb7a322c2843d66bd20380d300c5d74fdeaad55ae5f0e71e0744a13a871fe","target":"graph","created_at":"2026-05-18T00:11:11Z","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 count ramified genus $g$, degree $d$ coverings of the projective line with with fixed branch locus and fixed ramification data. Double Hurwitz numbers count such covers, where we fix two special profiles over $0$ and $\\infty$ and only simple ramification else. These objects feature insteresting structural behaviour and connections to geometry. In this paper, we introduce the notion of pruned double Hurwitz numbers, generalizing the notion of pruned simple Hurwitz numbers in \\cite{DN13}. We show that pruned double Hurwitz numbers, similar to usual double Hurwitz numbers, satisfy","authors_text":"Marvin Anas Hahn","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-12-05T00:20:48Z","title":"Pruned double Hurwitz numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01598","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":"sha256:44d9b70cf3041d150f4a5e2ac2f2232ac4a60adafedbbf5789a3aa066440d4d4","target":"record","created_at":"2026-05-18T00:11:11Z","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":"c126f8eec1208f95aff0aceacabcc1fb416ff522ed4b7f3b1d4c947f3304ccf2","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-12-05T00:20:48Z","title_canon_sha256":"1d163df063ad487f4f55f803d479a99d768d250fa3ca533e64d8041484ff62e8"},"schema_version":"1.0","source":{"id":"1512.01598","kind":"arxiv","version":2}},"canonical_sha256":"1e98543ed6f00e35dd41388beb082ed01913d8896447167792370e7a9b2d2ee7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1e98543ed6f00e35dd41388beb082ed01913d8896447167792370e7a9b2d2ee7","first_computed_at":"2026-05-18T00:11:11.944632Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:11.944632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9DpQbPvw1/OOIZFxBO2CXTdxz4e1V/UbkS1TB5CqheFxw3bubHTg+VL0hIgyTomucBpGSjM9UzzIFD7cBVEVAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:11.945338Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.01598","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:44d9b70cf3041d150f4a5e2ac2f2232ac4a60adafedbbf5789a3aa066440d4d4","sha256:44abb7a322c2843d66bd20380d300c5d74fdeaad55ae5f0e71e0744a13a871fe"],"state_sha256":"bf3dc660da6d789230fb939e5a7c49c445dbbd6a02596186897198b31ceb89db"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"95NJlwfjNF3m23Ni+impxWat1NyjkAYRmQjmSigMDl50Q1S0ar+vRXIuW0C6Z8JK3COa6IyKQ7RUZz54nOvUDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T13:03:01.984941Z","bundle_sha256":"6d77ddf30d734f7c556bb8aba420b9eb6f9de0cb3a0bf30d252d30fc3ac3c1d1"}}