{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:WKQSJ7XTDQTTIN64KHDYUIWSR3","short_pith_number":"pith:WKQSJ7XT","canonical_record":{"source":{"id":"1504.07449","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-04-28T12:35:42Z","cross_cats_sorted":[],"title_canon_sha256":"6dbaa3c97ad566f87c875157c1c50decf2d6affde37b8d0d5d39ef42c0144288","abstract_canon_sha256":"4593e37f7f5a6bd244f77a90bd53d5498f36f49fac3edffbde9c60122d819bf1"},"schema_version":"1.0"},"canonical_sha256":"b2a124fef31c273437dc51c78a22d28edc484395469a9d0fdb4c30aeb9a4ccd2","source":{"kind":"arxiv","id":"1504.07449","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.07449","created_at":"2026-05-18T00:46:02Z"},{"alias_kind":"arxiv_version","alias_value":"1504.07449v5","created_at":"2026-05-18T00:46:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.07449","created_at":"2026-05-18T00:46:02Z"},{"alias_kind":"pith_short_12","alias_value":"WKQSJ7XTDQTT","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WKQSJ7XTDQTTIN64","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WKQSJ7XT","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:WKQSJ7XTDQTTIN64KHDYUIWSR3","target":"record","payload":{"canonical_record":{"source":{"id":"1504.07449","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-04-28T12:35:42Z","cross_cats_sorted":[],"title_canon_sha256":"6dbaa3c97ad566f87c875157c1c50decf2d6affde37b8d0d5d39ef42c0144288","abstract_canon_sha256":"4593e37f7f5a6bd244f77a90bd53d5498f36f49fac3edffbde9c60122d819bf1"},"schema_version":"1.0"},"canonical_sha256":"b2a124fef31c273437dc51c78a22d28edc484395469a9d0fdb4c30aeb9a4ccd2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:02.866437Z","signature_b64":"HxI5pWQUt5FmsIcYjzdPDax4GF4SXN/QJWOzbt0l7MZ0NhgyCFFIQKoxTe4S4T7NyAZVAQ5gwfwtJpN0mAQUAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b2a124fef31c273437dc51c78a22d28edc484395469a9d0fdb4c30aeb9a4ccd2","last_reissued_at":"2026-05-18T00:46:02.866037Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:02.866037Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.07449","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:46:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eZycDBzUZy23R9M8k1mpUsPuu+T7NcJRTFEaZ5aqNvkbiftF6K4/DklmleEnR3d3oqcu26uh36s8c5XVEcR1Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T08:57:11.026736Z"},"content_sha256":"151d7dee636ecc3baaea1b39ffa22641e543bec87c96a1ee65e645bb50a3fce2","schema_version":"1.0","event_id":"sha256:151d7dee636ecc3baaea1b39ffa22641e543bec87c96a1ee65e645bb50a3fce2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:WKQSJ7XTDQTTIN64KHDYUIWSR3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the first cohomology of automorphism groups of graph groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Conchita Mart\\'inez-P\\'erez, Javier Aramayona","submitted_at":"2015-04-28T12:35:42Z","abstract_excerpt":"We study the (virtual) indicability of the automorphism group $Aut(A_\\Gamma)$ of the right-angled Artin group $A_\\Gamma$ associated to a simplicial graph $\\Gamma$. First, we identify two conditions -- denoted (B1) and (B2) -- on $\\Gamma$ which together imply that $H^1(G, Z)=0$ for certain finite-index subgroups $G<Aut(A_\\Gamma)$. On the other hand we will show that (B2) is equivalent to the matrix group ${\\mathcal H} = {\\rm Im}(Aut(A_\\Gamma) \\to Aut(H_1(A_\\Gamma))) <GL(n,Z)$ not being virtually indicable, and also to $\\mathcal H$ having Kazhdan's property (T). As a consequence, $Aut(A_\\Gamma)$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.07449","kind":"arxiv","version":5},"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":"2026-05-18T00:46:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"US+l+tve+kJaev6uOdF1i7M0QfLKKq/IFyFEkGl9DZfnyi1dF/IQJXmtzhAquqgjDdXTx23PIWTbhXj7vmaGDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T08:57:11.027079Z"},"content_sha256":"e1f9dd317b4267b529408652bb962834949abe4a7075a5ede868c5d1a47ce843","schema_version":"1.0","event_id":"sha256:e1f9dd317b4267b529408652bb962834949abe4a7075a5ede868c5d1a47ce843"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WKQSJ7XTDQTTIN64KHDYUIWSR3/bundle.json","state_url":"https://pith.science/pith/WKQSJ7XTDQTTIN64KHDYUIWSR3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WKQSJ7XTDQTTIN64KHDYUIWSR3/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":"2026-06-03T08:57:11Z","links":{"resolver":"https://pith.science/pith/WKQSJ7XTDQTTIN64KHDYUIWSR3","bundle":"https://pith.science/pith/WKQSJ7XTDQTTIN64KHDYUIWSR3/bundle.json","state":"https://pith.science/pith/WKQSJ7XTDQTTIN64KHDYUIWSR3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WKQSJ7XTDQTTIN64KHDYUIWSR3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:WKQSJ7XTDQTTIN64KHDYUIWSR3","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":"4593e37f7f5a6bd244f77a90bd53d5498f36f49fac3edffbde9c60122d819bf1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-04-28T12:35:42Z","title_canon_sha256":"6dbaa3c97ad566f87c875157c1c50decf2d6affde37b8d0d5d39ef42c0144288"},"schema_version":"1.0","source":{"id":"1504.07449","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.07449","created_at":"2026-05-18T00:46:02Z"},{"alias_kind":"arxiv_version","alias_value":"1504.07449v5","created_at":"2026-05-18T00:46:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.07449","created_at":"2026-05-18T00:46:02Z"},{"alias_kind":"pith_short_12","alias_value":"WKQSJ7XTDQTT","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WKQSJ7XTDQTTIN64","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WKQSJ7XT","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:e1f9dd317b4267b529408652bb962834949abe4a7075a5ede868c5d1a47ce843","target":"graph","created_at":"2026-05-18T00:46:02Z","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":"We study the (virtual) indicability of the automorphism group $Aut(A_\\Gamma)$ of the right-angled Artin group $A_\\Gamma$ associated to a simplicial graph $\\Gamma$. First, we identify two conditions -- denoted (B1) and (B2) -- on $\\Gamma$ which together imply that $H^1(G, Z)=0$ for certain finite-index subgroups $G<Aut(A_\\Gamma)$. On the other hand we will show that (B2) is equivalent to the matrix group ${\\mathcal H} = {\\rm Im}(Aut(A_\\Gamma) \\to Aut(H_1(A_\\Gamma))) <GL(n,Z)$ not being virtually indicable, and also to $\\mathcal H$ having Kazhdan's property (T). As a consequence, $Aut(A_\\Gamma)$","authors_text":"Conchita Mart\\'inez-P\\'erez, Javier Aramayona","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-04-28T12:35:42Z","title":"On the first cohomology of automorphism groups of graph groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.07449","kind":"arxiv","version":5},"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":"sha256:151d7dee636ecc3baaea1b39ffa22641e543bec87c96a1ee65e645bb50a3fce2","target":"record","created_at":"2026-05-18T00:46:02Z","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":"4593e37f7f5a6bd244f77a90bd53d5498f36f49fac3edffbde9c60122d819bf1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-04-28T12:35:42Z","title_canon_sha256":"6dbaa3c97ad566f87c875157c1c50decf2d6affde37b8d0d5d39ef42c0144288"},"schema_version":"1.0","source":{"id":"1504.07449","kind":"arxiv","version":5}},"canonical_sha256":"b2a124fef31c273437dc51c78a22d28edc484395469a9d0fdb4c30aeb9a4ccd2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b2a124fef31c273437dc51c78a22d28edc484395469a9d0fdb4c30aeb9a4ccd2","first_computed_at":"2026-05-18T00:46:02.866037Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:02.866037Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HxI5pWQUt5FmsIcYjzdPDax4GF4SXN/QJWOzbt0l7MZ0NhgyCFFIQKoxTe4S4T7NyAZVAQ5gwfwtJpN0mAQUAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:02.866437Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.07449","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:151d7dee636ecc3baaea1b39ffa22641e543bec87c96a1ee65e645bb50a3fce2","sha256:e1f9dd317b4267b529408652bb962834949abe4a7075a5ede868c5d1a47ce843"],"state_sha256":"122a2e275997872770d76f0a7eaeec2f1864544c58e5f32aed348e6739fe5c6d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yCG0hNuJp3VllV5GRWH2kb98DmF1a0FOKBis2Qhnj8xsexp9eI8teb4kHTplACpFGU7eUhicc5BSzzdtnOBcDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T08:57:11.028958Z","bundle_sha256":"483dfcb135a8fa6e20266e1edb6bd0ff139431df052d2e3388be9d32114a3604"}}