{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:QHWPKFYYRSL76U2WV6AJ3TW2G6","short_pith_number":"pith:QHWPKFYY","canonical_record":{"source":{"id":"1607.05148","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-07-18T15:58:12Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"998390cf48b7f758beb1f5abe2cb11d9c8e9edd2bc5f1478ad1d09abefec24a4","abstract_canon_sha256":"c76639bc8d6fed960fd409f8cb082c08ebee2d8d846df3cded530f8924c60626"},"schema_version":"1.0"},"canonical_sha256":"81ecf517188c97ff5356af809dceda379ed3234aeba45f0e72b7378fe4928957","source":{"kind":"arxiv","id":"1607.05148","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.05148","created_at":"2026-05-18T00:39:40Z"},{"alias_kind":"arxiv_version","alias_value":"1607.05148v2","created_at":"2026-05-18T00:39:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.05148","created_at":"2026-05-18T00:39:40Z"},{"alias_kind":"pith_short_12","alias_value":"QHWPKFYYRSL7","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QHWPKFYYRSL76U2W","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QHWPKFYY","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:QHWPKFYYRSL76U2WV6AJ3TW2G6","target":"record","payload":{"canonical_record":{"source":{"id":"1607.05148","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-07-18T15:58:12Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"998390cf48b7f758beb1f5abe2cb11d9c8e9edd2bc5f1478ad1d09abefec24a4","abstract_canon_sha256":"c76639bc8d6fed960fd409f8cb082c08ebee2d8d846df3cded530f8924c60626"},"schema_version":"1.0"},"canonical_sha256":"81ecf517188c97ff5356af809dceda379ed3234aeba45f0e72b7378fe4928957","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:40.342334Z","signature_b64":"6eI1Weq50pbUQJGV87Oq7Q8VpT67wSjPUxMz6sGiMBPbGhyvd5ZsnwRA1SPVrH253xl8XM/7FAwcQ79x0QtaDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81ecf517188c97ff5356af809dceda379ed3234aeba45f0e72b7378fe4928957","last_reissued_at":"2026-05-18T00:39:40.341685Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:40.341685Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.05148","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":"2026-05-18T00:39:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XTH8ajwarzwUv2iAH6HV4gPx3Je0/MJCP+h+tSAAPe7UHkovDIIYVvwv9NQ1h4wjDOU7qNd05Xt09QF/cpRaCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T10:55:47.346288Z"},"content_sha256":"63b45aa8bea6d846cc6a49d7eced29ad7e2cd50894136f38713f14117b094fb4","schema_version":"1.0","event_id":"sha256:63b45aa8bea6d846cc6a49d7eced29ad7e2cd50894136f38713f14117b094fb4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:QHWPKFYYRSL76U2WV6AJ3TW2G6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Frobenius algebras and homotopy fixed points of group actions on bicategories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.QA","authors_text":"Alessandro Valentino, Christoph Schweigert, Jan Hesse","submitted_at":"2016-07-18T15:58:12Z","abstract_excerpt":"We explicitly show that symmetric Frobenius structures on a finite-dimensional, semi-simple algebra stand in bijection to homotopy fixed points of the trivial SO(2)-action on the bicategory of finite-dimensional, semi-simple algebras, bimodules and intertwiners. The results are motivated by the 2-dimensional Cobordism Hypothesis for oriented manifolds, and can hence be interpreted in the realm of Topological Quantum Field Theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05148","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":"2026-05-18T00:39:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Je0qHFLHxYQrXDdekNnwX5fPUzWH7bdWTZkb4gFmLCoV3mohTroouom4YKYlN8XPCNuLZOJzjlmA5FsH0tYyAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T10:55:47.346634Z"},"content_sha256":"3a29f40a76a06829208a83b507dbb5c90f8798e3f48a41e575c16b16182bf6c1","schema_version":"1.0","event_id":"sha256:3a29f40a76a06829208a83b507dbb5c90f8798e3f48a41e575c16b16182bf6c1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QHWPKFYYRSL76U2WV6AJ3TW2G6/bundle.json","state_url":"https://pith.science/pith/QHWPKFYYRSL76U2WV6AJ3TW2G6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QHWPKFYYRSL76U2WV6AJ3TW2G6/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":"2026-06-09T10:55:47Z","links":{"resolver":"https://pith.science/pith/QHWPKFYYRSL76U2WV6AJ3TW2G6","bundle":"https://pith.science/pith/QHWPKFYYRSL76U2WV6AJ3TW2G6/bundle.json","state":"https://pith.science/pith/QHWPKFYYRSL76U2WV6AJ3TW2G6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QHWPKFYYRSL76U2WV6AJ3TW2G6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QHWPKFYYRSL76U2WV6AJ3TW2G6","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":"c76639bc8d6fed960fd409f8cb082c08ebee2d8d846df3cded530f8924c60626","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-07-18T15:58:12Z","title_canon_sha256":"998390cf48b7f758beb1f5abe2cb11d9c8e9edd2bc5f1478ad1d09abefec24a4"},"schema_version":"1.0","source":{"id":"1607.05148","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.05148","created_at":"2026-05-18T00:39:40Z"},{"alias_kind":"arxiv_version","alias_value":"1607.05148v2","created_at":"2026-05-18T00:39:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.05148","created_at":"2026-05-18T00:39:40Z"},{"alias_kind":"pith_short_12","alias_value":"QHWPKFYYRSL7","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QHWPKFYYRSL76U2W","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QHWPKFYY","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:3a29f40a76a06829208a83b507dbb5c90f8798e3f48a41e575c16b16182bf6c1","target":"graph","created_at":"2026-05-18T00:39:40Z","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 explicitly show that symmetric Frobenius structures on a finite-dimensional, semi-simple algebra stand in bijection to homotopy fixed points of the trivial SO(2)-action on the bicategory of finite-dimensional, semi-simple algebras, bimodules and intertwiners. The results are motivated by the 2-dimensional Cobordism Hypothesis for oriented manifolds, and can hence be interpreted in the realm of Topological Quantum Field Theory.","authors_text":"Alessandro Valentino, Christoph Schweigert, Jan Hesse","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-07-18T15:58:12Z","title":"Frobenius algebras and homotopy fixed points of group actions on bicategories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05148","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":"sha256:63b45aa8bea6d846cc6a49d7eced29ad7e2cd50894136f38713f14117b094fb4","target":"record","created_at":"2026-05-18T00:39:40Z","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":"c76639bc8d6fed960fd409f8cb082c08ebee2d8d846df3cded530f8924c60626","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-07-18T15:58:12Z","title_canon_sha256":"998390cf48b7f758beb1f5abe2cb11d9c8e9edd2bc5f1478ad1d09abefec24a4"},"schema_version":"1.0","source":{"id":"1607.05148","kind":"arxiv","version":2}},"canonical_sha256":"81ecf517188c97ff5356af809dceda379ed3234aeba45f0e72b7378fe4928957","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81ecf517188c97ff5356af809dceda379ed3234aeba45f0e72b7378fe4928957","first_computed_at":"2026-05-18T00:39:40.341685Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:40.341685Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6eI1Weq50pbUQJGV87Oq7Q8VpT67wSjPUxMz6sGiMBPbGhyvd5ZsnwRA1SPVrH253xl8XM/7FAwcQ79x0QtaDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:40.342334Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.05148","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63b45aa8bea6d846cc6a49d7eced29ad7e2cd50894136f38713f14117b094fb4","sha256:3a29f40a76a06829208a83b507dbb5c90f8798e3f48a41e575c16b16182bf6c1"],"state_sha256":"e9a5521b9dbe9b6338691c58a09c143e7cc27ceccb8f585fde47d8165222e2a7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1gtf+6EG5WERKTDaUpSYCFlhGRCVubQoCIBT611YeQYwIDNylPQlNXp/MOgaPpNalHJq5FRL4Qi3nHIm+3x+BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T10:55:47.348436Z","bundle_sha256":"5dffd4423bfe13f339a8cdcb521008e4e9c0af2db69660d29a3742a2d2d2bdbe"}}