{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:5WEZWP5CHCX45XDQKBR2W4Z3VW","short_pith_number":"pith:5WEZWP5C","canonical_record":{"source":{"id":"1109.5248","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-09-24T09:37:55Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"c661c563d74401648b2f024d834e30eef053f99c8610dc07589eeb4988076f8f","abstract_canon_sha256":"daf0309fbb7cef89b6dfa19962023d85ee5f9851630c83e3a57d4d088ffe4936"},"schema_version":"1.0"},"canonical_sha256":"ed899b3fa238afcedc705063ab733bad8fcabd7faf494f2e218967485772070c","source":{"kind":"arxiv","id":"1109.5248","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.5248","created_at":"2026-05-18T02:47:31Z"},{"alias_kind":"arxiv_version","alias_value":"1109.5248v3","created_at":"2026-05-18T02:47:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5248","created_at":"2026-05-18T02:47:31Z"},{"alias_kind":"pith_short_12","alias_value":"5WEZWP5CHCX4","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5WEZWP5CHCX45XDQ","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5WEZWP5C","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:5WEZWP5CHCX45XDQKBR2W4Z3VW","target":"record","payload":{"canonical_record":{"source":{"id":"1109.5248","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-09-24T09:37:55Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"c661c563d74401648b2f024d834e30eef053f99c8610dc07589eeb4988076f8f","abstract_canon_sha256":"daf0309fbb7cef89b6dfa19962023d85ee5f9851630c83e3a57d4d088ffe4936"},"schema_version":"1.0"},"canonical_sha256":"ed899b3fa238afcedc705063ab733bad8fcabd7faf494f2e218967485772070c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:31.801629Z","signature_b64":"a/sJNzllOEyfgoTTeBO1XwQhrnKtabi0cJPlsi1FwpTe1UCrUfAxNJwz5qK2tnMlmlE1vfh4kHnaJsbqmtokAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed899b3fa238afcedc705063ab733bad8fcabd7faf494f2e218967485772070c","last_reissued_at":"2026-05-18T02:47:31.801027Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:31.801027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.5248","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:47:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mNtTpEBpdSeFKOVm76kdZcgthpiPDk9EM5xXLcJycr5OGQ8Gdsg9brfJg2vTHZDY9JPTuSCre8uh+DL6vLP8Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T07:47:49.494868Z"},"content_sha256":"8557584c0adbbd2b64714474c379eb700ae379e98edaf7b98c10059b88808850","schema_version":"1.0","event_id":"sha256:8557584c0adbbd2b64714474c379eb700ae379e98edaf7b98c10059b88808850"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:5WEZWP5CHCX45XDQKBR2W4Z3VW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fox pairings and generalized Dehn twists","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Gwenael Massuyeau, Vladimir Turaev","submitted_at":"2011-09-24T09:37:55Z","abstract_excerpt":"We introduce a notion of a Fox pairing in a group algebra and use Fox pairings to define automorphisms of the Malcev completions of groups. These automorphisms generalize to the algebraic setting the action of the Dehn twists in the group algebras of the fundamental groups of surfaces. This work is inspired by the Kawazumi-Kuno generalization of the Dehn twists to non-simple closed curves on surfaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5248","kind":"arxiv","version":3},"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":"2026-05-18T02:47:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oTg44fPhquE53Tc9YOTSFfb0uXXoDJ/ZfWEUcukd5r8/8QJ41eP3Xvlpl3E318UgxHFiJOQUD6Q9VUV3mA2WCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T07:47:49.495214Z"},"content_sha256":"c0ae83d038ada4cd5353b4453bf4b1cba3849a79285c128201647e92655e84b9","schema_version":"1.0","event_id":"sha256:c0ae83d038ada4cd5353b4453bf4b1cba3849a79285c128201647e92655e84b9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5WEZWP5CHCX45XDQKBR2W4Z3VW/bundle.json","state_url":"https://pith.science/pith/5WEZWP5CHCX45XDQKBR2W4Z3VW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5WEZWP5CHCX45XDQKBR2W4Z3VW/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":"2026-06-05T07:47:49Z","links":{"resolver":"https://pith.science/pith/5WEZWP5CHCX45XDQKBR2W4Z3VW","bundle":"https://pith.science/pith/5WEZWP5CHCX45XDQKBR2W4Z3VW/bundle.json","state":"https://pith.science/pith/5WEZWP5CHCX45XDQKBR2W4Z3VW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5WEZWP5CHCX45XDQKBR2W4Z3VW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:5WEZWP5CHCX45XDQKBR2W4Z3VW","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":"daf0309fbb7cef89b6dfa19962023d85ee5f9851630c83e3a57d4d088ffe4936","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-09-24T09:37:55Z","title_canon_sha256":"c661c563d74401648b2f024d834e30eef053f99c8610dc07589eeb4988076f8f"},"schema_version":"1.0","source":{"id":"1109.5248","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.5248","created_at":"2026-05-18T02:47:31Z"},{"alias_kind":"arxiv_version","alias_value":"1109.5248v3","created_at":"2026-05-18T02:47:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5248","created_at":"2026-05-18T02:47:31Z"},{"alias_kind":"pith_short_12","alias_value":"5WEZWP5CHCX4","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5WEZWP5CHCX45XDQ","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5WEZWP5C","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:c0ae83d038ada4cd5353b4453bf4b1cba3849a79285c128201647e92655e84b9","target":"graph","created_at":"2026-05-18T02:47:31Z","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 introduce a notion of a Fox pairing in a group algebra and use Fox pairings to define automorphisms of the Malcev completions of groups. These automorphisms generalize to the algebraic setting the action of the Dehn twists in the group algebras of the fundamental groups of surfaces. This work is inspired by the Kawazumi-Kuno generalization of the Dehn twists to non-simple closed curves on surfaces.","authors_text":"Gwenael Massuyeau, Vladimir Turaev","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-09-24T09:37:55Z","title":"Fox pairings and generalized Dehn twists"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5248","kind":"arxiv","version":3},"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":"sha256:8557584c0adbbd2b64714474c379eb700ae379e98edaf7b98c10059b88808850","target":"record","created_at":"2026-05-18T02:47:31Z","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":"daf0309fbb7cef89b6dfa19962023d85ee5f9851630c83e3a57d4d088ffe4936","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-09-24T09:37:55Z","title_canon_sha256":"c661c563d74401648b2f024d834e30eef053f99c8610dc07589eeb4988076f8f"},"schema_version":"1.0","source":{"id":"1109.5248","kind":"arxiv","version":3}},"canonical_sha256":"ed899b3fa238afcedc705063ab733bad8fcabd7faf494f2e218967485772070c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ed899b3fa238afcedc705063ab733bad8fcabd7faf494f2e218967485772070c","first_computed_at":"2026-05-18T02:47:31.801027Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:31.801027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a/sJNzllOEyfgoTTeBO1XwQhrnKtabi0cJPlsi1FwpTe1UCrUfAxNJwz5qK2tnMlmlE1vfh4kHnaJsbqmtokAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:31.801629Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.5248","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8557584c0adbbd2b64714474c379eb700ae379e98edaf7b98c10059b88808850","sha256:c0ae83d038ada4cd5353b4453bf4b1cba3849a79285c128201647e92655e84b9"],"state_sha256":"3c16faa19b91ababaeb5a01c00d545399a7eb4800658642c5f5365d5cbbeecaa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SIcc0f+kJeTGwgQTbEFTcOHAGm+MEMHqldy6PSXQjJQ8lp3KuU5284uXaXppu4+vFfYoC+SP8+SZJFGAlRyJAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T07:47:49.497932Z","bundle_sha256":"171de52538c1cb72b81c0ee962994aef5738f460c39cfcfc581832e38113dcea"}}