{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1995:VFLCE6L7XMACUX252BY4XIUYKW","short_pith_number":"pith:VFLCE6L7","canonical_record":{"source":{"id":"dg-ga/9511008","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"dg-ga","submitted_at":"1995-11-18T00:18:52Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"b7af18563c10f8c6fcbc1ae761a61398efe348feebaa7d077b4c901f96ac0cda","abstract_canon_sha256":"56ca19e1e63209bf3cd1e7ed8e35fa9569bf0547fd47355707cba3c8abaef56b"},"schema_version":"1.0"},"canonical_sha256":"a95622797fbb002a5f5dd071cba298559150765c4b99672ef89b64752e7a8308","source":{"kind":"arxiv","id":"dg-ga/9511008","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"dg-ga/9511008","created_at":"2026-07-04T15:08:43Z"},{"alias_kind":"arxiv_version","alias_value":"dg-ga/9511008v1","created_at":"2026-07-04T15:08:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.dg-ga/9511008","created_at":"2026-07-04T15:08:43Z"},{"alias_kind":"pith_short_12","alias_value":"VFLCE6L7XMAC","created_at":"2026-07-04T15:08:43Z"},{"alias_kind":"pith_short_16","alias_value":"VFLCE6L7XMACUX25","created_at":"2026-07-04T15:08:43Z"},{"alias_kind":"pith_short_8","alias_value":"VFLCE6L7","created_at":"2026-07-04T15:08:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1995:VFLCE6L7XMACUX252BY4XIUYKW","target":"record","payload":{"canonical_record":{"source":{"id":"dg-ga/9511008","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"dg-ga","submitted_at":"1995-11-18T00:18:52Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"b7af18563c10f8c6fcbc1ae761a61398efe348feebaa7d077b4c901f96ac0cda","abstract_canon_sha256":"56ca19e1e63209bf3cd1e7ed8e35fa9569bf0547fd47355707cba3c8abaef56b"},"schema_version":"1.0"},"canonical_sha256":"a95622797fbb002a5f5dd071cba298559150765c4b99672ef89b64752e7a8308","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:08:43.193777Z","signature_b64":"GAPW6FJCwciNHdwrNrEMH2NhMhE1wjJGrPbEn8qDOSdmR2qFY/E+I1NTs4TNGzTMmgy7H/JQREUFm/fbvIMdCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a95622797fbb002a5f5dd071cba298559150765c4b99672ef89b64752e7a8308","last_reissued_at":"2026-07-04T15:08:43.193387Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:08:43.193387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"dg-ga/9511008","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":"2026-07-04T15:08:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8bIE1sKLXTKeKpRc59okAPFHfG8q9ubDyo2RUGg41J2kf0HgRK1MXHnkL8rNENTjehgQChlIQPNVT/3M+PeGBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T19:27:50.886122Z"},"content_sha256":"7fb43f2f492556ae990fb173dfbb3652b57d27b0ce6c2eacac18aee08f3b0670","schema_version":"1.0","event_id":"sha256:7fb43f2f492556ae990fb173dfbb3652b57d27b0ce6c2eacac18aee08f3b0670"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1995:VFLCE6L7XMACUX252BY4XIUYKW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hamiltonian torus actions on symplectic orbifolds and toric varieties","license":"","headline":"","cross_cats":["math.DG"],"primary_cat":"dg-ga","authors_text":"Eugene Lerman (MIT, presently Univ. of Illinois at Urban-Champaign), Susan Tolman (MIT)","submitted_at":"1995-11-18T00:18:52Z","abstract_excerpt":"In the first part of the paper, we build a foundation for further work on Hamiltonian actions on symplectic orbifolds. Most importantly we prove the orbifold versions of the abelian connectedness and convexity theorems.\n  In the second half, we prove that compact symplectic orbifolds with completely integrable torus actions are classified by convex simple rational polytopes with a positive integer attached to each facet and that all such orbifolds are algebraic toric varieties."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"dg-ga/9511008","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/dg-ga/9511008/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":"2026-07-04T15:08:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9iDZhxtHj0wKYYjqe6UA/5wNAUpMM+lnJ+497XUcnZMIpBTfsAbJTX26IVdMIUbBYoJIMiYsQFY6/8hGn/RBDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T19:27:50.886667Z"},"content_sha256":"182b43d76523565842315bbb80b881dac04d17d7dc79bf17f2e7ce97ed122c86","schema_version":"1.0","event_id":"sha256:182b43d76523565842315bbb80b881dac04d17d7dc79bf17f2e7ce97ed122c86"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VFLCE6L7XMACUX252BY4XIUYKW/bundle.json","state_url":"https://pith.science/pith/VFLCE6L7XMACUX252BY4XIUYKW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VFLCE6L7XMACUX252BY4XIUYKW/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":"2026-08-12T19:27:50Z","links":{"resolver":"https://pith.science/pith/VFLCE6L7XMACUX252BY4XIUYKW","bundle":"https://pith.science/pith/VFLCE6L7XMACUX252BY4XIUYKW/bundle.json","state":"https://pith.science/pith/VFLCE6L7XMACUX252BY4XIUYKW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VFLCE6L7XMACUX252BY4XIUYKW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1995:VFLCE6L7XMACUX252BY4XIUYKW","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":"56ca19e1e63209bf3cd1e7ed8e35fa9569bf0547fd47355707cba3c8abaef56b","cross_cats_sorted":["math.DG"],"license":"","primary_cat":"dg-ga","submitted_at":"1995-11-18T00:18:52Z","title_canon_sha256":"b7af18563c10f8c6fcbc1ae761a61398efe348feebaa7d077b4c901f96ac0cda"},"schema_version":"1.0","source":{"id":"dg-ga/9511008","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"dg-ga/9511008","created_at":"2026-07-04T15:08:43Z"},{"alias_kind":"arxiv_version","alias_value":"dg-ga/9511008v1","created_at":"2026-07-04T15:08:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.dg-ga/9511008","created_at":"2026-07-04T15:08:43Z"},{"alias_kind":"pith_short_12","alias_value":"VFLCE6L7XMAC","created_at":"2026-07-04T15:08:43Z"},{"alias_kind":"pith_short_16","alias_value":"VFLCE6L7XMACUX25","created_at":"2026-07-04T15:08:43Z"},{"alias_kind":"pith_short_8","alias_value":"VFLCE6L7","created_at":"2026-07-04T15:08:43Z"}],"graph_snapshots":[{"event_id":"sha256:182b43d76523565842315bbb80b881dac04d17d7dc79bf17f2e7ce97ed122c86","target":"graph","created_at":"2026-07-04T15:08:43Z","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/dg-ga/9511008/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In the first part of the paper, we build a foundation for further work on Hamiltonian actions on symplectic orbifolds. Most importantly we prove the orbifold versions of the abelian connectedness and convexity theorems.\n  In the second half, we prove that compact symplectic orbifolds with completely integrable torus actions are classified by convex simple rational polytopes with a positive integer attached to each facet and that all such orbifolds are algebraic toric varieties.","authors_text":"Eugene Lerman (MIT, presently Univ. of Illinois at Urban-Champaign), Susan Tolman (MIT)","cross_cats":["math.DG"],"headline":"","license":"","primary_cat":"dg-ga","submitted_at":"1995-11-18T00:18:52Z","title":"Hamiltonian torus actions on symplectic orbifolds and toric varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"dg-ga/9511008","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":"sha256:7fb43f2f492556ae990fb173dfbb3652b57d27b0ce6c2eacac18aee08f3b0670","target":"record","created_at":"2026-07-04T15:08:43Z","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":"56ca19e1e63209bf3cd1e7ed8e35fa9569bf0547fd47355707cba3c8abaef56b","cross_cats_sorted":["math.DG"],"license":"","primary_cat":"dg-ga","submitted_at":"1995-11-18T00:18:52Z","title_canon_sha256":"b7af18563c10f8c6fcbc1ae761a61398efe348feebaa7d077b4c901f96ac0cda"},"schema_version":"1.0","source":{"id":"dg-ga/9511008","kind":"arxiv","version":1}},"canonical_sha256":"a95622797fbb002a5f5dd071cba298559150765c4b99672ef89b64752e7a8308","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a95622797fbb002a5f5dd071cba298559150765c4b99672ef89b64752e7a8308","first_computed_at":"2026-07-04T15:08:43.193387Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:08:43.193387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GAPW6FJCwciNHdwrNrEMH2NhMhE1wjJGrPbEn8qDOSdmR2qFY/E+I1NTs4TNGzTMmgy7H/JQREUFm/fbvIMdCw==","signature_status":"signed_v1","signed_at":"2026-07-04T15:08:43.193777Z","signed_message":"canonical_sha256_bytes"},"source_id":"dg-ga/9511008","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7fb43f2f492556ae990fb173dfbb3652b57d27b0ce6c2eacac18aee08f3b0670","sha256:182b43d76523565842315bbb80b881dac04d17d7dc79bf17f2e7ce97ed122c86"],"state_sha256":"846bf23f7882c19b1d9fc7a1dc01efa97641ed1deb4dc1d55cc86362f08f814c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"539dRx+N/YeSmwljbhDNe8DcCnc88Xbt0c4DpF663hjQ3eL9+pUThAOrbaU4hrmlzR8wU9gHEFTDY4R/vuGPAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T19:27:50.891129Z","bundle_sha256":"f5f3982ca4c9b56ec702c6778f2c1edcb1b51b850f31a702d673c8c155e326d1"}}