{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:6F62AKME4EQOK77J6RB46AP7LK","short_pith_number":"pith:6F62AKME","canonical_record":{"source":{"id":"2010.00932","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2020-10-02T11:51:46Z","cross_cats_sorted":["cond-mat.str-el","hep-th"],"title_canon_sha256":"eea50051ad754232ea3a941d96a31e4eb1d18ae134afa1484ae90ac04f55faca","abstract_canon_sha256":"5fe7cc2acdff0c02dde5b8dc742af12bf84f7f7287f7c6aaf2d40a8e61ac855b"},"schema_version":"1.0"},"canonical_sha256":"f17da02984e120e57fe9f443cf01ff5aad0f97afeefc224b0ddc0c9d2aa3a65d","source":{"kind":"arxiv","id":"2010.00932","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.00932","created_at":"2026-07-05T01:39:49Z"},{"alias_kind":"arxiv_version","alias_value":"2010.00932v1","created_at":"2026-07-05T01:39:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.00932","created_at":"2026-07-05T01:39:49Z"},{"alias_kind":"pith_short_12","alias_value":"6F62AKME4EQO","created_at":"2026-07-05T01:39:49Z"},{"alias_kind":"pith_short_16","alias_value":"6F62AKME4EQOK77J","created_at":"2026-07-05T01:39:49Z"},{"alias_kind":"pith_short_8","alias_value":"6F62AKME","created_at":"2026-07-05T01:39:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:6F62AKME4EQOK77J6RB46AP7LK","target":"record","payload":{"canonical_record":{"source":{"id":"2010.00932","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2020-10-02T11:51:46Z","cross_cats_sorted":["cond-mat.str-el","hep-th"],"title_canon_sha256":"eea50051ad754232ea3a941d96a31e4eb1d18ae134afa1484ae90ac04f55faca","abstract_canon_sha256":"5fe7cc2acdff0c02dde5b8dc742af12bf84f7f7287f7c6aaf2d40a8e61ac855b"},"schema_version":"1.0"},"canonical_sha256":"f17da02984e120e57fe9f443cf01ff5aad0f97afeefc224b0ddc0c9d2aa3a65d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:39:49.050394Z","signature_b64":"sfRk6CMG7YYiwmn3S8PjfY1hhaQeHTG6XPGYijHp3A+JLnFGdlKxtJonoAQnzDztTz4u81yEpQHswc0Yl/fbDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f17da02984e120e57fe9f443cf01ff5aad0f97afeefc224b0ddc0c9d2aa3a65d","last_reissued_at":"2026-07-05T01:39:49.049889Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:39:49.049889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2010.00932","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":"2026-07-05T01:39:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AXdnWaxYmSlQJB01z7dbyBVZxHmZNnXXLZE8HK8AgE1PM4KIi2hoh1UmGkCf2ZdHZBoFkd24mgMZQ8xq2ZVDDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T18:36:18.269733Z"},"content_sha256":"50e0490d911650fb3746dbd7ff4726b420649f0ff5890329cf8da38a11f8bea9","schema_version":"1.0","event_id":"sha256:50e0490d911650fb3746dbd7ff4726b420649f0ff5890329cf8da38a11f8bea9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:6F62AKME4EQOK77J6RB46AP7LK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fibonacci-type orbifold data in Ising modular categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el","hep-th"],"primary_cat":"math.QA","authors_text":"Ingo Runkel, Vincentas Mulevicius","submitted_at":"2020-10-02T11:51:46Z","abstract_excerpt":"An orbifold datum is a collection $\\mathbb{A}$ of algebraic data in a modular fusion category $\\mathcal{C}$. It allows one to define a new modular fusion category $\\mathcal{C}_{\\mathbb{A}}$ in a construction that is a generalisation of taking the Drinfeld centre of a fusion category. Under certain simplifying assumptions we characterise orbifold data $\\mathbb{A}$ in terms of scalars satisfying polynomial equations and give an explicit expression which computes the number of isomorphism classes of simple objects in $\\mathcal{C}_{\\mathbb{A}}$.\n  In Ising-type modular categories we find new examp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.00932","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2010.00932/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T01:39:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oJaPDnm8qD4VLYqNr67WCXpM4t5yXPwl4ygifZKjY3uwbSt1Hozvu2UvXi8wrHbmdS3cg1lAxvJ1nSEW97QtBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T18:36:18.270522Z"},"content_sha256":"2048a6ff1be9d049171c99a88c2a041c407056600263a08372d1ee6c5b23bc23","schema_version":"1.0","event_id":"sha256:2048a6ff1be9d049171c99a88c2a041c407056600263a08372d1ee6c5b23bc23"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6F62AKME4EQOK77J6RB46AP7LK/bundle.json","state_url":"https://pith.science/pith/6F62AKME4EQOK77J6RB46AP7LK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6F62AKME4EQOK77J6RB46AP7LK/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":"2026-08-07T18:36:18Z","links":{"resolver":"https://pith.science/pith/6F62AKME4EQOK77J6RB46AP7LK","bundle":"https://pith.science/pith/6F62AKME4EQOK77J6RB46AP7LK/bundle.json","state":"https://pith.science/pith/6F62AKME4EQOK77J6RB46AP7LK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6F62AKME4EQOK77J6RB46AP7LK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:6F62AKME4EQOK77J6RB46AP7LK","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":"5fe7cc2acdff0c02dde5b8dc742af12bf84f7f7287f7c6aaf2d40a8e61ac855b","cross_cats_sorted":["cond-mat.str-el","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2020-10-02T11:51:46Z","title_canon_sha256":"eea50051ad754232ea3a941d96a31e4eb1d18ae134afa1484ae90ac04f55faca"},"schema_version":"1.0","source":{"id":"2010.00932","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.00932","created_at":"2026-07-05T01:39:49Z"},{"alias_kind":"arxiv_version","alias_value":"2010.00932v1","created_at":"2026-07-05T01:39:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.00932","created_at":"2026-07-05T01:39:49Z"},{"alias_kind":"pith_short_12","alias_value":"6F62AKME4EQO","created_at":"2026-07-05T01:39:49Z"},{"alias_kind":"pith_short_16","alias_value":"6F62AKME4EQOK77J","created_at":"2026-07-05T01:39:49Z"},{"alias_kind":"pith_short_8","alias_value":"6F62AKME","created_at":"2026-07-05T01:39:49Z"}],"graph_snapshots":[{"event_id":"sha256:2048a6ff1be9d049171c99a88c2a041c407056600263a08372d1ee6c5b23bc23","target":"graph","created_at":"2026-07-05T01:39:49Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2010.00932/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"An orbifold datum is a collection $\\mathbb{A}$ of algebraic data in a modular fusion category $\\mathcal{C}$. It allows one to define a new modular fusion category $\\mathcal{C}_{\\mathbb{A}}$ in a construction that is a generalisation of taking the Drinfeld centre of a fusion category. Under certain simplifying assumptions we characterise orbifold data $\\mathbb{A}$ in terms of scalars satisfying polynomial equations and give an explicit expression which computes the number of isomorphism classes of simple objects in $\\mathcal{C}_{\\mathbb{A}}$.\n  In Ising-type modular categories we find new examp","authors_text":"Ingo Runkel, Vincentas Mulevicius","cross_cats":["cond-mat.str-el","hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2020-10-02T11:51:46Z","title":"Fibonacci-type orbifold data in Ising modular categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.00932","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":"sha256:50e0490d911650fb3746dbd7ff4726b420649f0ff5890329cf8da38a11f8bea9","target":"record","created_at":"2026-07-05T01:39:49Z","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":"5fe7cc2acdff0c02dde5b8dc742af12bf84f7f7287f7c6aaf2d40a8e61ac855b","cross_cats_sorted":["cond-mat.str-el","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2020-10-02T11:51:46Z","title_canon_sha256":"eea50051ad754232ea3a941d96a31e4eb1d18ae134afa1484ae90ac04f55faca"},"schema_version":"1.0","source":{"id":"2010.00932","kind":"arxiv","version":1}},"canonical_sha256":"f17da02984e120e57fe9f443cf01ff5aad0f97afeefc224b0ddc0c9d2aa3a65d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f17da02984e120e57fe9f443cf01ff5aad0f97afeefc224b0ddc0c9d2aa3a65d","first_computed_at":"2026-07-05T01:39:49.049889Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:39:49.049889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sfRk6CMG7YYiwmn3S8PjfY1hhaQeHTG6XPGYijHp3A+JLnFGdlKxtJonoAQnzDztTz4u81yEpQHswc0Yl/fbDg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:39:49.050394Z","signed_message":"canonical_sha256_bytes"},"source_id":"2010.00932","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50e0490d911650fb3746dbd7ff4726b420649f0ff5890329cf8da38a11f8bea9","sha256:2048a6ff1be9d049171c99a88c2a041c407056600263a08372d1ee6c5b23bc23"],"state_sha256":"279892fe493834bf9b769a3870861d39635850dde4b3b1faf8ce71cab23e569d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mqHGSzsFm1XYuOyTBYOg/t50n1xs28y3w7erXHy53z/2zc/ZtsmU3LGFOcSYnB6H+Ae9KMlLpaklLilGfK1tCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T18:36:18.274552Z","bundle_sha256":"5afcbbbe85e649eb459d7243608e715feb59ae6d44542b5639b673a45bb51d44"}}