{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:NWHRPCI62JZ3VH2UBLRQRXPWBM","short_pith_number":"pith:NWHRPCI6","canonical_record":{"source":{"id":"2212.11573","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-12-22T09:57:09Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"2cf1f3282f66f9ea42026af1d2eae963b8e872f8a01d2297a2bcd93a9c9184a6","abstract_canon_sha256":"5a71122c60120348a200b474cfa63a7959bab322c1a84060ff85953654c7a67c"},"schema_version":"1.0"},"canonical_sha256":"6d8f17891ed273ba9f540ae308ddf60b3a3a184880b04a1867417042f2a1f6b5","source":{"kind":"arxiv","id":"2212.11573","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.11573","created_at":"2026-05-26T02:03:44Z"},{"alias_kind":"arxiv_version","alias_value":"2212.11573v3","created_at":"2026-05-26T02:03:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.11573","created_at":"2026-05-26T02:03:44Z"},{"alias_kind":"pith_short_12","alias_value":"NWHRPCI62JZ3","created_at":"2026-05-26T02:03:44Z"},{"alias_kind":"pith_short_16","alias_value":"NWHRPCI62JZ3VH2U","created_at":"2026-05-26T02:03:44Z"},{"alias_kind":"pith_short_8","alias_value":"NWHRPCI6","created_at":"2026-05-26T02:03:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:NWHRPCI62JZ3VH2UBLRQRXPWBM","target":"record","payload":{"canonical_record":{"source":{"id":"2212.11573","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-12-22T09:57:09Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"2cf1f3282f66f9ea42026af1d2eae963b8e872f8a01d2297a2bcd93a9c9184a6","abstract_canon_sha256":"5a71122c60120348a200b474cfa63a7959bab322c1a84060ff85953654c7a67c"},"schema_version":"1.0"},"canonical_sha256":"6d8f17891ed273ba9f540ae308ddf60b3a3a184880b04a1867417042f2a1f6b5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T02:03:44.217130Z","signature_b64":"zLhx8XHg8vQ4lbxoTbf9niy/G86YvESRzR4QxGtB43oGuhY4im7nIrgXX8oO6sTrQAV88GnA1ZWPgLU1UVh2CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d8f17891ed273ba9f540ae308ddf60b3a3a184880b04a1867417042f2a1f6b5","last_reissued_at":"2026-05-26T02:03:44.216264Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T02:03:44.216264Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2212.11573","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":"2026-05-26T02:03:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pzlfyd4SfAbC/Lrx2hiVSt8CjIeXOZfBzY53+ndgTadiXbSOJSUPqSCdyluyzYI1X7YyzTCnBlwtyAGd/TesAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:33:53.678931Z"},"content_sha256":"5ed02ca82b0f453d31e02a7c056eafa4cf62868c8d0b868f44e2feca09e826fd","schema_version":"1.0","event_id":"sha256:5ed02ca82b0f453d31e02a7c056eafa4cf62868c8d0b868f44e2feca09e826fd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:NWHRPCI62JZ3VH2UBLRQRXPWBM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Modelling interface factorizations between Landau-Ginzburg models as module functors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Stefan Fredenhagen","submitted_at":"2022-12-22T09:57:09Z","abstract_excerpt":"We study the fusion of B-type interfaces between N=(2,2) supersymmetric Landau-Ginzburg models. Such interfaces can be described by matrix factorizations of the difference of the superpotentials, and their fusion is modelled by the tensor product of the factorizations. The effect of fusing a fixed interface gives rise to a functor on the category of matrix factorizations. For at least some interfaces, this can be lifted to a functor on the category of modules over polynomial rings. These fusion functors provide an alternative way of modelling a class of interfaces between Landau-Ginzburg model"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.11573","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2212.11573/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":"2026-05-26T02:03:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lY7LzKpzPtx0cEhuZ6G85epgjkwbAFS0N88H050hpVLw8OqyyPpySsQBvBX0F5+rALQXSJAW6zan+USN5JpgBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:33:53.679300Z"},"content_sha256":"ad7349be56d2cdaa4a2b5e7752d10c46e8c9c6b0d1c89b5504c6583022aba55f","schema_version":"1.0","event_id":"sha256:ad7349be56d2cdaa4a2b5e7752d10c46e8c9c6b0d1c89b5504c6583022aba55f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NWHRPCI62JZ3VH2UBLRQRXPWBM/bundle.json","state_url":"https://pith.science/pith/NWHRPCI62JZ3VH2UBLRQRXPWBM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NWHRPCI62JZ3VH2UBLRQRXPWBM/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":"2026-06-01T21:33:53Z","links":{"resolver":"https://pith.science/pith/NWHRPCI62JZ3VH2UBLRQRXPWBM","bundle":"https://pith.science/pith/NWHRPCI62JZ3VH2UBLRQRXPWBM/bundle.json","state":"https://pith.science/pith/NWHRPCI62JZ3VH2UBLRQRXPWBM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NWHRPCI62JZ3VH2UBLRQRXPWBM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:NWHRPCI62JZ3VH2UBLRQRXPWBM","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":"5a71122c60120348a200b474cfa63a7959bab322c1a84060ff85953654c7a67c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-12-22T09:57:09Z","title_canon_sha256":"2cf1f3282f66f9ea42026af1d2eae963b8e872f8a01d2297a2bcd93a9c9184a6"},"schema_version":"1.0","source":{"id":"2212.11573","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.11573","created_at":"2026-05-26T02:03:44Z"},{"alias_kind":"arxiv_version","alias_value":"2212.11573v3","created_at":"2026-05-26T02:03:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.11573","created_at":"2026-05-26T02:03:44Z"},{"alias_kind":"pith_short_12","alias_value":"NWHRPCI62JZ3","created_at":"2026-05-26T02:03:44Z"},{"alias_kind":"pith_short_16","alias_value":"NWHRPCI62JZ3VH2U","created_at":"2026-05-26T02:03:44Z"},{"alias_kind":"pith_short_8","alias_value":"NWHRPCI6","created_at":"2026-05-26T02:03:44Z"}],"graph_snapshots":[{"event_id":"sha256:ad7349be56d2cdaa4a2b5e7752d10c46e8c9c6b0d1c89b5504c6583022aba55f","target":"graph","created_at":"2026-05-26T02:03:44Z","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/2212.11573/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the fusion of B-type interfaces between N=(2,2) supersymmetric Landau-Ginzburg models. Such interfaces can be described by matrix factorizations of the difference of the superpotentials, and their fusion is modelled by the tensor product of the factorizations. The effect of fusing a fixed interface gives rise to a functor on the category of matrix factorizations. For at least some interfaces, this can be lifted to a functor on the category of modules over polynomial rings. These fusion functors provide an alternative way of modelling a class of interfaces between Landau-Ginzburg model","authors_text":"Stefan Fredenhagen","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-12-22T09:57:09Z","title":"Modelling interface factorizations between Landau-Ginzburg models as module functors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.11573","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":"sha256:5ed02ca82b0f453d31e02a7c056eafa4cf62868c8d0b868f44e2feca09e826fd","target":"record","created_at":"2026-05-26T02:03:44Z","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":"5a71122c60120348a200b474cfa63a7959bab322c1a84060ff85953654c7a67c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-12-22T09:57:09Z","title_canon_sha256":"2cf1f3282f66f9ea42026af1d2eae963b8e872f8a01d2297a2bcd93a9c9184a6"},"schema_version":"1.0","source":{"id":"2212.11573","kind":"arxiv","version":3}},"canonical_sha256":"6d8f17891ed273ba9f540ae308ddf60b3a3a184880b04a1867417042f2a1f6b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d8f17891ed273ba9f540ae308ddf60b3a3a184880b04a1867417042f2a1f6b5","first_computed_at":"2026-05-26T02:03:44.216264Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T02:03:44.216264Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zLhx8XHg8vQ4lbxoTbf9niy/G86YvESRzR4QxGtB43oGuhY4im7nIrgXX8oO6sTrQAV88GnA1ZWPgLU1UVh2CA==","signature_status":"signed_v1","signed_at":"2026-05-26T02:03:44.217130Z","signed_message":"canonical_sha256_bytes"},"source_id":"2212.11573","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ed02ca82b0f453d31e02a7c056eafa4cf62868c8d0b868f44e2feca09e826fd","sha256:ad7349be56d2cdaa4a2b5e7752d10c46e8c9c6b0d1c89b5504c6583022aba55f"],"state_sha256":"29a3923189a4eb6671a34a455844dec04c016044d71b4f6355b25699cfd79e22"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c+SkyhJWVxroYK90oznW5phv6ttKzTZl9aywLVrrh0XBLm64Z1lnHkQg74+aPN5m2Ks8DWexDd3iIn7gQS6PDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T21:33:53.681256Z","bundle_sha256":"53831096d25c262de391e283db4fd300f82f07642b564ab48075c38fe59818d6"}}