{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:2VNFEVB7IIIQOUDS5VHFPSYMJJ","short_pith_number":"pith:2VNFEVB7","canonical_record":{"source":{"id":"1512.01447","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-12-04T15:16:47Z","cross_cats_sorted":[],"title_canon_sha256":"15c74a98a5e8f7bfacd6b4531f2a177860580fd0c2f2c2c0b8d709c5ddab13ca","abstract_canon_sha256":"f4225c081b77de39316847990ded2be00d10f97a9eb5192d6c2f837fd9466041"},"schema_version":"1.0"},"canonical_sha256":"d55a52543f4211075072ed4e57cb0c4a49d09e320213b1c0699e3f322333b333","source":{"kind":"arxiv","id":"1512.01447","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.01447","created_at":"2026-05-18T00:08:05Z"},{"alias_kind":"arxiv_version","alias_value":"1512.01447v2","created_at":"2026-05-18T00:08:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.01447","created_at":"2026-05-18T00:08:05Z"},{"alias_kind":"pith_short_12","alias_value":"2VNFEVB7IIIQ","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2VNFEVB7IIIQOUDS","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2VNFEVB7","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:2VNFEVB7IIIQOUDS5VHFPSYMJJ","target":"record","payload":{"canonical_record":{"source":{"id":"1512.01447","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-12-04T15:16:47Z","cross_cats_sorted":[],"title_canon_sha256":"15c74a98a5e8f7bfacd6b4531f2a177860580fd0c2f2c2c0b8d709c5ddab13ca","abstract_canon_sha256":"f4225c081b77de39316847990ded2be00d10f97a9eb5192d6c2f837fd9466041"},"schema_version":"1.0"},"canonical_sha256":"d55a52543f4211075072ed4e57cb0c4a49d09e320213b1c0699e3f322333b333","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:05.442986Z","signature_b64":"Yhkk8j/J6sLxbrXgQFcMEFZj4AHgt7TZvU+ymYeqNLTmGn+F6Iy+C+WdRn+vUIf8yxTKn/RGuswlEyznZoyCDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d55a52543f4211075072ed4e57cb0c4a49d09e320213b1c0699e3f322333b333","last_reissued_at":"2026-05-18T00:08:05.442515Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:05.442515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.01447","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":"2026-05-18T00:08:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zXCCnsl+AH0azysch6bw5dEx28cu8xG3NlAzEzWmfwMSaYzGYLOVyL1QlTQUdZLyiDlxxxXKSVg4xG/RB9QSBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T04:12:49.640429Z"},"content_sha256":"7a52bc4f9df04b704b1905b139c3f2b4c6aba55fa31be27a9630671481cc3a85","schema_version":"1.0","event_id":"sha256:7a52bc4f9df04b704b1905b139c3f2b4c6aba55fa31be27a9630671481cc3a85"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:2VNFEVB7IIIQOUDS5VHFPSYMJJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Independence of $\\ell$ for the supports in the Decomposition Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Shenghao Sun","submitted_at":"2015-12-04T15:16:47Z","abstract_excerpt":"In this note, we prove a result on the independence of $\\ell$ for the supports of irreducible perverse sheaves occurring in the Decomposition Theorem, as well as for the family of local systems on each support. It generalizes Gabber's result on the independence of $\\ell$ of intersection cohomology to the relative case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01447","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":"2026-05-18T00:08:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PcO7jspCmBsiCEBGR9FbJEvzVafrf99HmK30h0lmW1vda1rwMK3yi2CSOOSF3zNW6VcWOQbVTKLIzP0AxzL8AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T04:12:49.641144Z"},"content_sha256":"9203f4f7d3ee2a2773b7f67c31dea2ce084067d82d905c301d35457e461b8f7e","schema_version":"1.0","event_id":"sha256:9203f4f7d3ee2a2773b7f67c31dea2ce084067d82d905c301d35457e461b8f7e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2VNFEVB7IIIQOUDS5VHFPSYMJJ/bundle.json","state_url":"https://pith.science/pith/2VNFEVB7IIIQOUDS5VHFPSYMJJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2VNFEVB7IIIQOUDS5VHFPSYMJJ/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":"2026-06-08T04:12:49Z","links":{"resolver":"https://pith.science/pith/2VNFEVB7IIIQOUDS5VHFPSYMJJ","bundle":"https://pith.science/pith/2VNFEVB7IIIQOUDS5VHFPSYMJJ/bundle.json","state":"https://pith.science/pith/2VNFEVB7IIIQOUDS5VHFPSYMJJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2VNFEVB7IIIQOUDS5VHFPSYMJJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2VNFEVB7IIIQOUDS5VHFPSYMJJ","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":"f4225c081b77de39316847990ded2be00d10f97a9eb5192d6c2f837fd9466041","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-12-04T15:16:47Z","title_canon_sha256":"15c74a98a5e8f7bfacd6b4531f2a177860580fd0c2f2c2c0b8d709c5ddab13ca"},"schema_version":"1.0","source":{"id":"1512.01447","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.01447","created_at":"2026-05-18T00:08:05Z"},{"alias_kind":"arxiv_version","alias_value":"1512.01447v2","created_at":"2026-05-18T00:08:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.01447","created_at":"2026-05-18T00:08:05Z"},{"alias_kind":"pith_short_12","alias_value":"2VNFEVB7IIIQ","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2VNFEVB7IIIQOUDS","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2VNFEVB7","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:9203f4f7d3ee2a2773b7f67c31dea2ce084067d82d905c301d35457e461b8f7e","target":"graph","created_at":"2026-05-18T00:08:05Z","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"},"paper":{"abstract_excerpt":"In this note, we prove a result on the independence of $\\ell$ for the supports of irreducible perverse sheaves occurring in the Decomposition Theorem, as well as for the family of local systems on each support. It generalizes Gabber's result on the independence of $\\ell$ of intersection cohomology to the relative case.","authors_text":"Shenghao Sun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-12-04T15:16:47Z","title":"Independence of $\\ell$ for the supports in the Decomposition Theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01447","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":"sha256:7a52bc4f9df04b704b1905b139c3f2b4c6aba55fa31be27a9630671481cc3a85","target":"record","created_at":"2026-05-18T00:08:05Z","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":"f4225c081b77de39316847990ded2be00d10f97a9eb5192d6c2f837fd9466041","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-12-04T15:16:47Z","title_canon_sha256":"15c74a98a5e8f7bfacd6b4531f2a177860580fd0c2f2c2c0b8d709c5ddab13ca"},"schema_version":"1.0","source":{"id":"1512.01447","kind":"arxiv","version":2}},"canonical_sha256":"d55a52543f4211075072ed4e57cb0c4a49d09e320213b1c0699e3f322333b333","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d55a52543f4211075072ed4e57cb0c4a49d09e320213b1c0699e3f322333b333","first_computed_at":"2026-05-18T00:08:05.442515Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:05.442515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Yhkk8j/J6sLxbrXgQFcMEFZj4AHgt7TZvU+ymYeqNLTmGn+F6Iy+C+WdRn+vUIf8yxTKn/RGuswlEyznZoyCDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:05.442986Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.01447","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a52bc4f9df04b704b1905b139c3f2b4c6aba55fa31be27a9630671481cc3a85","sha256:9203f4f7d3ee2a2773b7f67c31dea2ce084067d82d905c301d35457e461b8f7e"],"state_sha256":"db5a4c385ac6e43092476f1f8873cbd6e2a7d730cbae89d50fff2c394db36a89"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ITZ6F9VEaGfxY3McqA1XGgYVJ2oSYzoGds7XWonCy+yoGuvadWqerviVRf4y9/24Uo+A5aaigmIjssE+CgMEDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T04:12:49.645555Z","bundle_sha256":"a3dce112d974f2da67cf6957ece3d1de380a8ccf5d316473456b6cc5588b0304"}}