{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:LRSYKX6LD5BXXZCFZ62BZB4T5A","short_pith_number":"pith:LRSYKX6L","canonical_record":{"source":{"id":"2209.08528","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AG","submitted_at":"2022-09-18T10:29:06Z","cross_cats_sorted":[],"title_canon_sha256":"d1ea2c208aeb56463bee886de1d3b91c5e1367054691f9263a97dd08ada54416","abstract_canon_sha256":"33635a516aff14caee0b27488a1ab494efabde45457c93824a651cecdd914859"},"schema_version":"1.0"},"canonical_sha256":"5c65855fcb1f437be445cfb41c8793e80998f376fa3c30a2e2140f730ccbe224","source":{"kind":"arxiv","id":"2209.08528","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.08528","created_at":"2026-07-05T12:05:05Z"},{"alias_kind":"arxiv_version","alias_value":"2209.08528v3","created_at":"2026-07-05T12:05:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.08528","created_at":"2026-07-05T12:05:05Z"},{"alias_kind":"pith_short_12","alias_value":"LRSYKX6LD5BX","created_at":"2026-07-05T12:05:05Z"},{"alias_kind":"pith_short_16","alias_value":"LRSYKX6LD5BXXZCF","created_at":"2026-07-05T12:05:05Z"},{"alias_kind":"pith_short_8","alias_value":"LRSYKX6L","created_at":"2026-07-05T12:05:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:LRSYKX6LD5BXXZCFZ62BZB4T5A","target":"record","payload":{"canonical_record":{"source":{"id":"2209.08528","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AG","submitted_at":"2022-09-18T10:29:06Z","cross_cats_sorted":[],"title_canon_sha256":"d1ea2c208aeb56463bee886de1d3b91c5e1367054691f9263a97dd08ada54416","abstract_canon_sha256":"33635a516aff14caee0b27488a1ab494efabde45457c93824a651cecdd914859"},"schema_version":"1.0"},"canonical_sha256":"5c65855fcb1f437be445cfb41c8793e80998f376fa3c30a2e2140f730ccbe224","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:05:05.676813Z","signature_b64":"meEPR4IjHUhxEOHMuEc8deoLYTE7mmNOb472Hi0BYzBx6+ukOCOZeRv+3zt3nx6eynEJIju7qgyeXjT/+LrnAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c65855fcb1f437be445cfb41c8793e80998f376fa3c30a2e2140f730ccbe224","last_reissued_at":"2026-07-05T12:05:05.676358Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:05:05.676358Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2209.08528","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T12:05:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jyiVHqlw52dzjfWnYPv/AP/Ghphf24Le4uspMBVfCNHiUjoE4sLn+xPePoLcSRERpDx9l3ouUyYy2nyMDCp2BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T08:05:31.021031Z"},"content_sha256":"c20421e5f467cc46125ea89d4bec4ec2baa8dc39a0fe476ee47644b043e0b1b0","schema_version":"1.0","event_id":"sha256:c20421e5f467cc46125ea89d4bec4ec2baa8dc39a0fe476ee47644b043e0b1b0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:LRSYKX6LD5BXXZCFZ62BZB4T5A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Arithmetic liftings and 2d TQFT for dormant opers of higher level","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Yasuhiro Wakabayashi","submitted_at":"2022-09-18T10:29:06Z","abstract_excerpt":"This manuscript represents an advance in the enumerative geometry of opers that takes the subject beyond our previous work. Motivated by a counting problem of linear differential equations in positive characteristic, we investigate the moduli space of opers from arithmetic and combinatorial points of view. We construct a compactified moduli space classifying dormant $\\mathrm{PGL}_n^{(N)}$-opers (i.e., dormant $\\mathrm{PGL}_n$-opers of level $N$) on pointed stable curves in characteristic $p>0$. One of the key results is the generic \\'{e}taleness of that space for $n=2$, which is proved by obta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.08528","kind":"arxiv","version":3},"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/2209.08528/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T12:05:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vekH6P6ak0QwwZKdl3KH2IFcq3RS3QfyidcIT+GfEZsDvfBn5goim2rH6czXO8xcbbhjOJ2ZcI354C96pOAkCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T08:05:31.021554Z"},"content_sha256":"193efeb98816a2370879bc0a95a6e8ffc1da45023452966335faac8f426ff557","schema_version":"1.0","event_id":"sha256:193efeb98816a2370879bc0a95a6e8ffc1da45023452966335faac8f426ff557"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LRSYKX6LD5BXXZCFZ62BZB4T5A/bundle.json","state_url":"https://pith.science/pith/LRSYKX6LD5BXXZCFZ62BZB4T5A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LRSYKX6LD5BXXZCFZ62BZB4T5A/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":"2026-08-07T08:05:31Z","links":{"resolver":"https://pith.science/pith/LRSYKX6LD5BXXZCFZ62BZB4T5A","bundle":"https://pith.science/pith/LRSYKX6LD5BXXZCFZ62BZB4T5A/bundle.json","state":"https://pith.science/pith/LRSYKX6LD5BXXZCFZ62BZB4T5A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LRSYKX6LD5BXXZCFZ62BZB4T5A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:LRSYKX6LD5BXXZCFZ62BZB4T5A","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":"33635a516aff14caee0b27488a1ab494efabde45457c93824a651cecdd914859","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AG","submitted_at":"2022-09-18T10:29:06Z","title_canon_sha256":"d1ea2c208aeb56463bee886de1d3b91c5e1367054691f9263a97dd08ada54416"},"schema_version":"1.0","source":{"id":"2209.08528","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.08528","created_at":"2026-07-05T12:05:05Z"},{"alias_kind":"arxiv_version","alias_value":"2209.08528v3","created_at":"2026-07-05T12:05:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.08528","created_at":"2026-07-05T12:05:05Z"},{"alias_kind":"pith_short_12","alias_value":"LRSYKX6LD5BX","created_at":"2026-07-05T12:05:05Z"},{"alias_kind":"pith_short_16","alias_value":"LRSYKX6LD5BXXZCF","created_at":"2026-07-05T12:05:05Z"},{"alias_kind":"pith_short_8","alias_value":"LRSYKX6L","created_at":"2026-07-05T12:05:05Z"}],"graph_snapshots":[{"event_id":"sha256:193efeb98816a2370879bc0a95a6e8ffc1da45023452966335faac8f426ff557","target":"graph","created_at":"2026-07-05T12:05:05Z","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/2209.08528/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This manuscript represents an advance in the enumerative geometry of opers that takes the subject beyond our previous work. Motivated by a counting problem of linear differential equations in positive characteristic, we investigate the moduli space of opers from arithmetic and combinatorial points of view. We construct a compactified moduli space classifying dormant $\\mathrm{PGL}_n^{(N)}$-opers (i.e., dormant $\\mathrm{PGL}_n$-opers of level $N$) on pointed stable curves in characteristic $p>0$. One of the key results is the generic \\'{e}taleness of that space for $n=2$, which is proved by obta","authors_text":"Yasuhiro Wakabayashi","cross_cats":[],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AG","submitted_at":"2022-09-18T10:29:06Z","title":"Arithmetic liftings and 2d TQFT for dormant opers of higher level"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.08528","kind":"arxiv","version":3},"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:c20421e5f467cc46125ea89d4bec4ec2baa8dc39a0fe476ee47644b043e0b1b0","target":"record","created_at":"2026-07-05T12:05:05Z","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":"33635a516aff14caee0b27488a1ab494efabde45457c93824a651cecdd914859","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AG","submitted_at":"2022-09-18T10:29:06Z","title_canon_sha256":"d1ea2c208aeb56463bee886de1d3b91c5e1367054691f9263a97dd08ada54416"},"schema_version":"1.0","source":{"id":"2209.08528","kind":"arxiv","version":3}},"canonical_sha256":"5c65855fcb1f437be445cfb41c8793e80998f376fa3c30a2e2140f730ccbe224","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5c65855fcb1f437be445cfb41c8793e80998f376fa3c30a2e2140f730ccbe224","first_computed_at":"2026-07-05T12:05:05.676358Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:05:05.676358Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"meEPR4IjHUhxEOHMuEc8deoLYTE7mmNOb472Hi0BYzBx6+ukOCOZeRv+3zt3nx6eynEJIju7qgyeXjT/+LrnAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T12:05:05.676813Z","signed_message":"canonical_sha256_bytes"},"source_id":"2209.08528","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c20421e5f467cc46125ea89d4bec4ec2baa8dc39a0fe476ee47644b043e0b1b0","sha256:193efeb98816a2370879bc0a95a6e8ffc1da45023452966335faac8f426ff557"],"state_sha256":"807d38b6196f0e077403813ff19439d198a4061397ca1734947c1efa94d2bb80"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SznClT/m/oqcExdXxmjHbSE74CCEZvPZMBN+YfmLE/J7aMeP5Sy/wQy38uopZ6HGsYJPLWlkq1OxuS/7Qt28Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T08:05:31.028382Z","bundle_sha256":"bf5eca92e3bae7e1dee87d3a307305d243d3bea905bca18db413fc8a6a08e3ff"}}