{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:VEIQCER5Z2MENKD5FKOTUWEIVG","short_pith_number":"pith:VEIQCER5","canonical_record":{"source":{"id":"1608.05454","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-08-18T23:33:26Z","cross_cats_sorted":["math-ph","math.DG","math.MP","math.RT"],"title_canon_sha256":"89128bb2018b7c082f87d67775beca2261138dc2157e73f8d9bde4e740441a7d","abstract_canon_sha256":"0ec7e54db4c1db8406dfc7e75de8b02cf1db4710d83e5b389cbde5f02dcff43d"},"schema_version":"1.0"},"canonical_sha256":"a91101123dce9846a87d2a9d3a5888a9b43e30873814dc11496622e48a1f57cf","source":{"kind":"arxiv","id":"1608.05454","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.05454","created_at":"2026-05-18T00:24:53Z"},{"alias_kind":"arxiv_version","alias_value":"1608.05454v3","created_at":"2026-05-18T00:24:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.05454","created_at":"2026-05-18T00:24:53Z"},{"alias_kind":"pith_short_12","alias_value":"VEIQCER5Z2ME","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VEIQCER5Z2MENKD5","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VEIQCER5","created_at":"2026-05-18T12:30:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:VEIQCER5Z2MENKD5FKOTUWEIVG","target":"record","payload":{"canonical_record":{"source":{"id":"1608.05454","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-08-18T23:33:26Z","cross_cats_sorted":["math-ph","math.DG","math.MP","math.RT"],"title_canon_sha256":"89128bb2018b7c082f87d67775beca2261138dc2157e73f8d9bde4e740441a7d","abstract_canon_sha256":"0ec7e54db4c1db8406dfc7e75de8b02cf1db4710d83e5b389cbde5f02dcff43d"},"schema_version":"1.0"},"canonical_sha256":"a91101123dce9846a87d2a9d3a5888a9b43e30873814dc11496622e48a1f57cf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:53.264969Z","signature_b64":"RjO4NyPrX+b04eKn0H3m8g5vEUhvn7Be9jfZvUoIUyfB+TaFFGS/Iz50FcG7AoT2dMtc17OQwuLpml1+yCGDDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a91101123dce9846a87d2a9d3a5888a9b43e30873814dc11496622e48a1f57cf","last_reissued_at":"2026-05-18T00:24:53.264184Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:53.264184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.05454","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":"2026-05-18T00:24:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gr1NnVvTSIi12qh1nelQ4JW+3lHSzLGDItAJ6xxn26DdvcLIzZTxn34dAqlB+W3b7yyzrC1gx6C6nFxU6DtzAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T01:39:59.530254Z"},"content_sha256":"baf29ab7d1048dedd55a7a0d639ccc954f485c803211c580c6465f5206c313b7","schema_version":"1.0","event_id":"sha256:baf29ab7d1048dedd55a7a0d639ccc954f485c803211c580c6465f5206c313b7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:VEIQCER5Z2MENKD5FKOTUWEIVG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Complete integrability of the parahoric Hitchin system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DG","math.MP","math.RT"],"primary_cat":"math.AG","authors_text":"David Baraglia, Masoud Kamgarpour, Rohith Varma","submitted_at":"2016-08-18T23:33:26Z","abstract_excerpt":"Let $\\mathcal{G}$ be a parahoric group scheme over a complex projective curve $X$ of genus greater than one. Let $\\mathrm{Bun}_{\\mathcal{G}}$ denote the moduli stack of $\\mathcal{G}$-torsors on $X$. We prove several results concerning the Hitchin map on $T^*\\!\\mathrm{Bun}_{\\mathcal{G}}$. We first show that the parahoric analogue of the global nilpotent cone is isotropic and use this to prove that $\\mathrm{Bun}_{\\mathcal{G}}$ is \"very good\" in the sense of Beilinson-Drinfeld. We then prove that the parahoric Hitchin map is a Poisson map whose generic fibres are abelian varieties. Together, thes"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05454","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":""},"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":"2026-05-18T00:24:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GwwTcx7tnOCrpzrqJl5EfeIx2MBLxI/EpEaSA18SLfitqZYO3ilet0GHdp2EcNouqmYLwGxuPkWJMn7F0DxJDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T01:39:59.530967Z"},"content_sha256":"01069c4000183bb2e9d033f172fde65eec70fe0d330e7a7a6606e1f3ccb2d021","schema_version":"1.0","event_id":"sha256:01069c4000183bb2e9d033f172fde65eec70fe0d330e7a7a6606e1f3ccb2d021"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VEIQCER5Z2MENKD5FKOTUWEIVG/bundle.json","state_url":"https://pith.science/pith/VEIQCER5Z2MENKD5FKOTUWEIVG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VEIQCER5Z2MENKD5FKOTUWEIVG/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":"2026-06-05T01:39:59Z","links":{"resolver":"https://pith.science/pith/VEIQCER5Z2MENKD5FKOTUWEIVG","bundle":"https://pith.science/pith/VEIQCER5Z2MENKD5FKOTUWEIVG/bundle.json","state":"https://pith.science/pith/VEIQCER5Z2MENKD5FKOTUWEIVG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VEIQCER5Z2MENKD5FKOTUWEIVG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VEIQCER5Z2MENKD5FKOTUWEIVG","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":"0ec7e54db4c1db8406dfc7e75de8b02cf1db4710d83e5b389cbde5f02dcff43d","cross_cats_sorted":["math-ph","math.DG","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-08-18T23:33:26Z","title_canon_sha256":"89128bb2018b7c082f87d67775beca2261138dc2157e73f8d9bde4e740441a7d"},"schema_version":"1.0","source":{"id":"1608.05454","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.05454","created_at":"2026-05-18T00:24:53Z"},{"alias_kind":"arxiv_version","alias_value":"1608.05454v3","created_at":"2026-05-18T00:24:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.05454","created_at":"2026-05-18T00:24:53Z"},{"alias_kind":"pith_short_12","alias_value":"VEIQCER5Z2ME","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VEIQCER5Z2MENKD5","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VEIQCER5","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:01069c4000183bb2e9d033f172fde65eec70fe0d330e7a7a6606e1f3ccb2d021","target":"graph","created_at":"2026-05-18T00:24:53Z","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":"Let $\\mathcal{G}$ be a parahoric group scheme over a complex projective curve $X$ of genus greater than one. Let $\\mathrm{Bun}_{\\mathcal{G}}$ denote the moduli stack of $\\mathcal{G}$-torsors on $X$. We prove several results concerning the Hitchin map on $T^*\\!\\mathrm{Bun}_{\\mathcal{G}}$. We first show that the parahoric analogue of the global nilpotent cone is isotropic and use this to prove that $\\mathrm{Bun}_{\\mathcal{G}}$ is \"very good\" in the sense of Beilinson-Drinfeld. We then prove that the parahoric Hitchin map is a Poisson map whose generic fibres are abelian varieties. Together, thes","authors_text":"David Baraglia, Masoud Kamgarpour, Rohith Varma","cross_cats":["math-ph","math.DG","math.MP","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-08-18T23:33:26Z","title":"Complete integrability of the parahoric Hitchin system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05454","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:baf29ab7d1048dedd55a7a0d639ccc954f485c803211c580c6465f5206c313b7","target":"record","created_at":"2026-05-18T00:24:53Z","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":"0ec7e54db4c1db8406dfc7e75de8b02cf1db4710d83e5b389cbde5f02dcff43d","cross_cats_sorted":["math-ph","math.DG","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-08-18T23:33:26Z","title_canon_sha256":"89128bb2018b7c082f87d67775beca2261138dc2157e73f8d9bde4e740441a7d"},"schema_version":"1.0","source":{"id":"1608.05454","kind":"arxiv","version":3}},"canonical_sha256":"a91101123dce9846a87d2a9d3a5888a9b43e30873814dc11496622e48a1f57cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a91101123dce9846a87d2a9d3a5888a9b43e30873814dc11496622e48a1f57cf","first_computed_at":"2026-05-18T00:24:53.264184Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:53.264184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RjO4NyPrX+b04eKn0H3m8g5vEUhvn7Be9jfZvUoIUyfB+TaFFGS/Iz50FcG7AoT2dMtc17OQwuLpml1+yCGDDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:53.264969Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.05454","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:baf29ab7d1048dedd55a7a0d639ccc954f485c803211c580c6465f5206c313b7","sha256:01069c4000183bb2e9d033f172fde65eec70fe0d330e7a7a6606e1f3ccb2d021"],"state_sha256":"7c671f863c48e402ba3365c58123bcb7fb510fcd2fc7a1a3c539c5bdc672befb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6NsHnAx72asNScSZucjibBFd89YVy1mb8q4ChKoYNkTkWeec0S8UtJgJisa1EUKgwgKl78XO1ASZp3fyCdS5DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T01:39:59.534726Z","bundle_sha256":"03a8dcbd7b7c52f7c0afe94e20ee9b37329573292c5ee77700087dae90c114d4"}}