{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:LGMZNZ5L62HSPFIRL2X6M5DH5Y","short_pith_number":"pith:LGMZNZ5L","canonical_record":{"source":{"id":"1603.08855","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-03-29T17:32:13Z","cross_cats_sorted":["math.QA","math.RT"],"title_canon_sha256":"f5fd0d01192238ae5366bf14ce6f1e87b7cb3623e651601bb651b3141ce39688","abstract_canon_sha256":"be1237122c0eb215cd14a68387cddbf604361214e18a31d1ad45ce5f0462f12b"},"schema_version":"1.0"},"canonical_sha256":"599996e7abf68f2795115eafe67467ee24d15b0c3af1f2b76b5135d41d611f9d","source":{"kind":"arxiv","id":"1603.08855","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.08855","created_at":"2026-05-18T00:45:06Z"},{"alias_kind":"arxiv_version","alias_value":"1603.08855v1","created_at":"2026-05-18T00:45:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.08855","created_at":"2026-05-18T00:45:06Z"},{"alias_kind":"pith_short_12","alias_value":"LGMZNZ5L62HS","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LGMZNZ5L62HSPFIR","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LGMZNZ5L","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:LGMZNZ5L62HSPFIRL2X6M5DH5Y","target":"record","payload":{"canonical_record":{"source":{"id":"1603.08855","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-03-29T17:32:13Z","cross_cats_sorted":["math.QA","math.RT"],"title_canon_sha256":"f5fd0d01192238ae5366bf14ce6f1e87b7cb3623e651601bb651b3141ce39688","abstract_canon_sha256":"be1237122c0eb215cd14a68387cddbf604361214e18a31d1ad45ce5f0462f12b"},"schema_version":"1.0"},"canonical_sha256":"599996e7abf68f2795115eafe67467ee24d15b0c3af1f2b76b5135d41d611f9d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:06.619568Z","signature_b64":"T3l7hR5tMAOPnkqr9By56/EivhNt3fbodMri2VNVFgmFptZcn+d4kQ48iPga+sHOmN/APHGiiWkBmhkHLHowBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"599996e7abf68f2795115eafe67467ee24d15b0c3af1f2b76b5135d41d611f9d","last_reissued_at":"2026-05-18T00:45:06.619183Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:06.619183Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.08855","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":"2026-05-18T00:45:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YmAyoYmpAt0hcmQcOE25GL3jZuRa8yVhqjV9szjdahl+ZbGpQVUCCNXTRRMpCLYR5J9vN9Rz/lK0BTJqd0e5Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T14:25:14.588056Z"},"content_sha256":"4de88d530a1aa5f601ae25b10cf48e5f80ad3886da8a9eb7340a522caa709f23","schema_version":"1.0","event_id":"sha256:4de88d530a1aa5f601ae25b10cf48e5f80ad3886da8a9eb7340a522caa709f23"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:LGMZNZ5L62HSPFIRL2X6M5DH5Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Commutative hairy graphs and representations of $Out(F_r)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RT"],"primary_cat":"math.AT","authors_text":"Thomas Willwacher, Victor Turchin","submitted_at":"2016-03-29T17:32:13Z","abstract_excerpt":"We express the hairy graph complexes computing the rational homotopy groups of long embeddings (modulo immersion) of R^m in R^n as \"decorated\" graph complexes associated to certain representations of the outer automorphism groups of free groups. This interpretation gives rise to a natural spectral sequence, which allows us to shed some light on the structure of the hairy graph cohomology. We also explain briefly the connection to the deformation theory of the little discs operads and some conclusions that this brings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08855","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":"2026-05-18T00:45:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"99uRPY+z2/aOG70FM6aPy7j/eBWn1DSoPbPBqVc+e4qGorYgJkMId3MGj4qNiKUESnF4v4N1EJ677mprccZKAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T14:25:14.588419Z"},"content_sha256":"e5c9cbe51a7d7586e785447c5b8591f4120d09d6c0ad74578dd1e0f6d0f0610b","schema_version":"1.0","event_id":"sha256:e5c9cbe51a7d7586e785447c5b8591f4120d09d6c0ad74578dd1e0f6d0f0610b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LGMZNZ5L62HSPFIRL2X6M5DH5Y/bundle.json","state_url":"https://pith.science/pith/LGMZNZ5L62HSPFIRL2X6M5DH5Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LGMZNZ5L62HSPFIRL2X6M5DH5Y/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":"2026-06-04T14:25:14Z","links":{"resolver":"https://pith.science/pith/LGMZNZ5L62HSPFIRL2X6M5DH5Y","bundle":"https://pith.science/pith/LGMZNZ5L62HSPFIRL2X6M5DH5Y/bundle.json","state":"https://pith.science/pith/LGMZNZ5L62HSPFIRL2X6M5DH5Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LGMZNZ5L62HSPFIRL2X6M5DH5Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LGMZNZ5L62HSPFIRL2X6M5DH5Y","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":"be1237122c0eb215cd14a68387cddbf604361214e18a31d1ad45ce5f0462f12b","cross_cats_sorted":["math.QA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-03-29T17:32:13Z","title_canon_sha256":"f5fd0d01192238ae5366bf14ce6f1e87b7cb3623e651601bb651b3141ce39688"},"schema_version":"1.0","source":{"id":"1603.08855","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.08855","created_at":"2026-05-18T00:45:06Z"},{"alias_kind":"arxiv_version","alias_value":"1603.08855v1","created_at":"2026-05-18T00:45:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.08855","created_at":"2026-05-18T00:45:06Z"},{"alias_kind":"pith_short_12","alias_value":"LGMZNZ5L62HS","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LGMZNZ5L62HSPFIR","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LGMZNZ5L","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:e5c9cbe51a7d7586e785447c5b8591f4120d09d6c0ad74578dd1e0f6d0f0610b","target":"graph","created_at":"2026-05-18T00:45:06Z","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 express the hairy graph complexes computing the rational homotopy groups of long embeddings (modulo immersion) of R^m in R^n as \"decorated\" graph complexes associated to certain representations of the outer automorphism groups of free groups. This interpretation gives rise to a natural spectral sequence, which allows us to shed some light on the structure of the hairy graph cohomology. We also explain briefly the connection to the deformation theory of the little discs operads and some conclusions that this brings.","authors_text":"Thomas Willwacher, Victor Turchin","cross_cats":["math.QA","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-03-29T17:32:13Z","title":"Commutative hairy graphs and representations of $Out(F_r)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08855","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":"sha256:4de88d530a1aa5f601ae25b10cf48e5f80ad3886da8a9eb7340a522caa709f23","target":"record","created_at":"2026-05-18T00:45:06Z","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":"be1237122c0eb215cd14a68387cddbf604361214e18a31d1ad45ce5f0462f12b","cross_cats_sorted":["math.QA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-03-29T17:32:13Z","title_canon_sha256":"f5fd0d01192238ae5366bf14ce6f1e87b7cb3623e651601bb651b3141ce39688"},"schema_version":"1.0","source":{"id":"1603.08855","kind":"arxiv","version":1}},"canonical_sha256":"599996e7abf68f2795115eafe67467ee24d15b0c3af1f2b76b5135d41d611f9d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"599996e7abf68f2795115eafe67467ee24d15b0c3af1f2b76b5135d41d611f9d","first_computed_at":"2026-05-18T00:45:06.619183Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:06.619183Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T3l7hR5tMAOPnkqr9By56/EivhNt3fbodMri2VNVFgmFptZcn+d4kQ48iPga+sHOmN/APHGiiWkBmhkHLHowBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:06.619568Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.08855","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4de88d530a1aa5f601ae25b10cf48e5f80ad3886da8a9eb7340a522caa709f23","sha256:e5c9cbe51a7d7586e785447c5b8591f4120d09d6c0ad74578dd1e0f6d0f0610b"],"state_sha256":"1ffb35eecc27a1cf519d37c3383ba043b488ddfa531961c660767931a52e3cb1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pax8RLcLvK8w1V4yqGUu32a5il7pIfyLPYvmf/mxS2rB4gn9TespPHQSuvHFo4zZ9w06IpanrEj02bNASaudDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T14:25:14.590761Z","bundle_sha256":"aa339afab7e821e13dddfc1f490ce9b0a7937c7abaaf90fc6072b5ff1b885318"}}