{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:LTKS4IZNWPVMPVC27ILWI5O2KI","short_pith_number":"pith:LTKS4IZN","canonical_record":{"source":{"id":"1107.4815","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-07-24T23:58:20Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"2a85848b92b65e86f1835a00142a6bbe3d623a699b0fad217684acb475302e4f","abstract_canon_sha256":"257d766b20f8aeed8b6550ffb2af39cf70b2b1c9739bafa3aa762643b797dac9"},"schema_version":"1.0"},"canonical_sha256":"5cd52e232db3eac7d45afa176475da522a9e95469d263acf9b2c1771628d4d45","source":{"kind":"arxiv","id":"1107.4815","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.4815","created_at":"2026-05-18T04:16:54Z"},{"alias_kind":"arxiv_version","alias_value":"1107.4815v1","created_at":"2026-05-18T04:16:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4815","created_at":"2026-05-18T04:16:54Z"},{"alias_kind":"pith_short_12","alias_value":"LTKS4IZNWPVM","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LTKS4IZNWPVMPVC2","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LTKS4IZN","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:LTKS4IZNWPVMPVC27ILWI5O2KI","target":"record","payload":{"canonical_record":{"source":{"id":"1107.4815","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-07-24T23:58:20Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"2a85848b92b65e86f1835a00142a6bbe3d623a699b0fad217684acb475302e4f","abstract_canon_sha256":"257d766b20f8aeed8b6550ffb2af39cf70b2b1c9739bafa3aa762643b797dac9"},"schema_version":"1.0"},"canonical_sha256":"5cd52e232db3eac7d45afa176475da522a9e95469d263acf9b2c1771628d4d45","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:16:54.570734Z","signature_b64":"XPaeWFI6YxZ4FzECZKNsX9dnhn7AFmLCGWuIgXFfGcsIoGo5O+AtYHlPTlq24oAX4BGBuF2VtkI+SefS5M0ZDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5cd52e232db3eac7d45afa176475da522a9e95469d263acf9b2c1771628d4d45","last_reissued_at":"2026-05-18T04:16:54.570133Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:16:54.570133Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.4815","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":"2026-05-18T04:16:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yEhLBU0EWMnphMWckEIoaCAkbEL2ilylwl0GmeM4o2v3GFGUDq4Q/YPOOyygXXmP0L3PKBIglMFBZBeF/El0Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T04:52:39.729169Z"},"content_sha256":"fcf14f27c6145cf6b1c3ed76140c62affaa271ae604d2704b758317fbdf1eda7","schema_version":"1.0","event_id":"sha256:fcf14f27c6145cf6b1c3ed76140c62affaa271ae604d2704b758317fbdf1eda7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:LTKS4IZNWPVMPVC27ILWI5O2KI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Representations of finite groups: Local cohomology and support","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.RT","authors_text":"Dave Benson, Henning Krause, Srikanth B. Iyengar","submitted_at":"2011-07-24T23:58:20Z","abstract_excerpt":"These are the notes from an Oberwolfach Seminar which we ran from 23--29 May 2010."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4815","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":""},"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":"2026-05-18T04:16:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l9IVnMb+IjxiaIBUV5swaZk1nWeooBcMvrrvS8+cD2UbVPN4sXQ56GinPFOFmww/rT2sLWk37fpuzy9BDq2LBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T04:52:39.729824Z"},"content_sha256":"f61119dfbbbd6997ae9e3db1aac3bee0567cd4188a1b34bdb9f91811553d191a","schema_version":"1.0","event_id":"sha256:f61119dfbbbd6997ae9e3db1aac3bee0567cd4188a1b34bdb9f91811553d191a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LTKS4IZNWPVMPVC27ILWI5O2KI/bundle.json","state_url":"https://pith.science/pith/LTKS4IZNWPVMPVC27ILWI5O2KI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LTKS4IZNWPVMPVC27ILWI5O2KI/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":"2026-06-12T04:52:39Z","links":{"resolver":"https://pith.science/pith/LTKS4IZNWPVMPVC27ILWI5O2KI","bundle":"https://pith.science/pith/LTKS4IZNWPVMPVC27ILWI5O2KI/bundle.json","state":"https://pith.science/pith/LTKS4IZNWPVMPVC27ILWI5O2KI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LTKS4IZNWPVMPVC27ILWI5O2KI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:LTKS4IZNWPVMPVC27ILWI5O2KI","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":"257d766b20f8aeed8b6550ffb2af39cf70b2b1c9739bafa3aa762643b797dac9","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-07-24T23:58:20Z","title_canon_sha256":"2a85848b92b65e86f1835a00142a6bbe3d623a699b0fad217684acb475302e4f"},"schema_version":"1.0","source":{"id":"1107.4815","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.4815","created_at":"2026-05-18T04:16:54Z"},{"alias_kind":"arxiv_version","alias_value":"1107.4815v1","created_at":"2026-05-18T04:16:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4815","created_at":"2026-05-18T04:16:54Z"},{"alias_kind":"pith_short_12","alias_value":"LTKS4IZNWPVM","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LTKS4IZNWPVMPVC2","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LTKS4IZN","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:f61119dfbbbd6997ae9e3db1aac3bee0567cd4188a1b34bdb9f91811553d191a","target":"graph","created_at":"2026-05-18T04:16:54Z","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":"These are the notes from an Oberwolfach Seminar which we ran from 23--29 May 2010.","authors_text":"Dave Benson, Henning Krause, Srikanth B. Iyengar","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-07-24T23:58:20Z","title":"Representations of finite groups: Local cohomology and support"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4815","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:fcf14f27c6145cf6b1c3ed76140c62affaa271ae604d2704b758317fbdf1eda7","target":"record","created_at":"2026-05-18T04:16:54Z","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":"257d766b20f8aeed8b6550ffb2af39cf70b2b1c9739bafa3aa762643b797dac9","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-07-24T23:58:20Z","title_canon_sha256":"2a85848b92b65e86f1835a00142a6bbe3d623a699b0fad217684acb475302e4f"},"schema_version":"1.0","source":{"id":"1107.4815","kind":"arxiv","version":1}},"canonical_sha256":"5cd52e232db3eac7d45afa176475da522a9e95469d263acf9b2c1771628d4d45","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5cd52e232db3eac7d45afa176475da522a9e95469d263acf9b2c1771628d4d45","first_computed_at":"2026-05-18T04:16:54.570133Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:16:54.570133Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XPaeWFI6YxZ4FzECZKNsX9dnhn7AFmLCGWuIgXFfGcsIoGo5O+AtYHlPTlq24oAX4BGBuF2VtkI+SefS5M0ZDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:16:54.570734Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.4815","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fcf14f27c6145cf6b1c3ed76140c62affaa271ae604d2704b758317fbdf1eda7","sha256:f61119dfbbbd6997ae9e3db1aac3bee0567cd4188a1b34bdb9f91811553d191a"],"state_sha256":"9ee45b1393d4e29db394adebd7ca6d67ba2f1ed322cb0c777b1fceb9cafd9a4c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dKpc3HgfZmMrvBWXp0E9W7ZCL9wWsxyoe0wTiLxtuj1FNj39SRLWUFBkWsMxYJKyqeavv6p90SWgFNLuFbBBCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T04:52:39.733021Z","bundle_sha256":"6b7dc4488d44dde43869aa4a8b6c737ee9e9803754aa332861a02cbc0b20d5f2"}}