{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:PV2SZPTXHWVJPNBX57ZOLI7C3U","short_pith_number":"pith:PV2SZPTX","canonical_record":{"source":{"id":"2502.06951","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2025-02-10T19:00:03Z","cross_cats_sorted":["math-ph","math.AG","math.MP","math.SG"],"title_canon_sha256":"c83cf6e813d0d22b6021221ca8935e07e27413826f69070e51f0e53d17a6a7d7","abstract_canon_sha256":"b4a8fcf07a9ca763eb3d3b169e948ab448ee51783658a7457f42b50652a753f5"},"schema_version":"1.0"},"canonical_sha256":"7d752cbe773daa97b437eff2e5a3e2dd3872dc9a5d91156c2c03eebd014bb23b","source":{"kind":"arxiv","id":"2502.06951","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.06951","created_at":"2026-07-05T12:11:15Z"},{"alias_kind":"arxiv_version","alias_value":"2502.06951v4","created_at":"2026-07-05T12:11:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.06951","created_at":"2026-07-05T12:11:15Z"},{"alias_kind":"pith_short_12","alias_value":"PV2SZPTXHWVJ","created_at":"2026-07-05T12:11:15Z"},{"alias_kind":"pith_short_16","alias_value":"PV2SZPTXHWVJPNBX","created_at":"2026-07-05T12:11:15Z"},{"alias_kind":"pith_short_8","alias_value":"PV2SZPTX","created_at":"2026-07-05T12:11:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:PV2SZPTXHWVJPNBX57ZOLI7C3U","target":"record","payload":{"canonical_record":{"source":{"id":"2502.06951","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2025-02-10T19:00:03Z","cross_cats_sorted":["math-ph","math.AG","math.MP","math.SG"],"title_canon_sha256":"c83cf6e813d0d22b6021221ca8935e07e27413826f69070e51f0e53d17a6a7d7","abstract_canon_sha256":"b4a8fcf07a9ca763eb3d3b169e948ab448ee51783658a7457f42b50652a753f5"},"schema_version":"1.0"},"canonical_sha256":"7d752cbe773daa97b437eff2e5a3e2dd3872dc9a5d91156c2c03eebd014bb23b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:11:15.487713Z","signature_b64":"JECgT/gTBw6ucscLyLGzSzKnMeBrxFN+Pc4xeU70Lf7du0QBt48rb5dOhXQOGJMw8qSEBsJanFn/LL/e/cogBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d752cbe773daa97b437eff2e5a3e2dd3872dc9a5d91156c2c03eebd014bb23b","last_reissued_at":"2026-07-05T12:11:15.487071Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:11:15.487071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.06951","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T12:11:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VApy6VX/zceWBAREeNW6FnXfIzlhtgX4dV3s0zENmbiOea/qDk8r3dECCkI19mDgZSzAHZBO2X894xg6+Bf+DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T18:59:15.156764Z"},"content_sha256":"d076bce6156ad46faacb1080e92b1f3fedfa51cf7ef45022333d6c426e19ed7c","schema_version":"1.0","event_id":"sha256:d076bce6156ad46faacb1080e92b1f3fedfa51cf7ef45022333d6c426e19ed7c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:PV2SZPTXHWVJPNBX57ZOLI7C3U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Advancements in Functorial Homological Mirror Symmetry","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.AG","math.MP","math.SG"],"primary_cat":"hep-th","authors_text":"Veronica Pasquarella","submitted_at":"2025-02-10T19:00:03Z","abstract_excerpt":"Mostly inspired by recent work by Katzarkov, Kontsevich, and Sheshmani, combined with previous work by Aganagic, Ooguri, Saulina and Vafa with regard to BPS black hole microstate counting in terms of topological field theory calculations, we will show how these tools can be applied to concrete setups arising from String Theory, and why the formalism of functorial Homological Mirror Symmetry needs to be further developed. A crucial ingredient will turn out being cobordism techniques for evaluating invariants."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.06951","kind":"arxiv","version":4},"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/2502.06951/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":"2026-07-05T12:11:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QYlunJQUmNySemgQVVdaloGVlNam0MpmDb9Hk3mMd0j720tW2YJB9Kqq8xpaNMPYYvMvh4mo4mMzZN57pYNHCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T18:59:15.157324Z"},"content_sha256":"0f158f2891af34c0dda8d97d83007ecacea3a1f3d063f69b759aec665d3a1ff1","schema_version":"1.0","event_id":"sha256:0f158f2891af34c0dda8d97d83007ecacea3a1f3d063f69b759aec665d3a1ff1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PV2SZPTXHWVJPNBX57ZOLI7C3U/bundle.json","state_url":"https://pith.science/pith/PV2SZPTXHWVJPNBX57ZOLI7C3U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PV2SZPTXHWVJPNBX57ZOLI7C3U/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":"2026-08-18T18:59:15Z","links":{"resolver":"https://pith.science/pith/PV2SZPTXHWVJPNBX57ZOLI7C3U","bundle":"https://pith.science/pith/PV2SZPTXHWVJPNBX57ZOLI7C3U/bundle.json","state":"https://pith.science/pith/PV2SZPTXHWVJPNBX57ZOLI7C3U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PV2SZPTXHWVJPNBX57ZOLI7C3U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:PV2SZPTXHWVJPNBX57ZOLI7C3U","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":"b4a8fcf07a9ca763eb3d3b169e948ab448ee51783658a7457f42b50652a753f5","cross_cats_sorted":["math-ph","math.AG","math.MP","math.SG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2025-02-10T19:00:03Z","title_canon_sha256":"c83cf6e813d0d22b6021221ca8935e07e27413826f69070e51f0e53d17a6a7d7"},"schema_version":"1.0","source":{"id":"2502.06951","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.06951","created_at":"2026-07-05T12:11:15Z"},{"alias_kind":"arxiv_version","alias_value":"2502.06951v4","created_at":"2026-07-05T12:11:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.06951","created_at":"2026-07-05T12:11:15Z"},{"alias_kind":"pith_short_12","alias_value":"PV2SZPTXHWVJ","created_at":"2026-07-05T12:11:15Z"},{"alias_kind":"pith_short_16","alias_value":"PV2SZPTXHWVJPNBX","created_at":"2026-07-05T12:11:15Z"},{"alias_kind":"pith_short_8","alias_value":"PV2SZPTX","created_at":"2026-07-05T12:11:15Z"}],"graph_snapshots":[{"event_id":"sha256:0f158f2891af34c0dda8d97d83007ecacea3a1f3d063f69b759aec665d3a1ff1","target":"graph","created_at":"2026-07-05T12:11:15Z","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/2502.06951/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Mostly inspired by recent work by Katzarkov, Kontsevich, and Sheshmani, combined with previous work by Aganagic, Ooguri, Saulina and Vafa with regard to BPS black hole microstate counting in terms of topological field theory calculations, we will show how these tools can be applied to concrete setups arising from String Theory, and why the formalism of functorial Homological Mirror Symmetry needs to be further developed. A crucial ingredient will turn out being cobordism techniques for evaluating invariants.","authors_text":"Veronica Pasquarella","cross_cats":["math-ph","math.AG","math.MP","math.SG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2025-02-10T19:00:03Z","title":"Advancements in Functorial Homological Mirror Symmetry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.06951","kind":"arxiv","version":4},"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:d076bce6156ad46faacb1080e92b1f3fedfa51cf7ef45022333d6c426e19ed7c","target":"record","created_at":"2026-07-05T12:11:15Z","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":"b4a8fcf07a9ca763eb3d3b169e948ab448ee51783658a7457f42b50652a753f5","cross_cats_sorted":["math-ph","math.AG","math.MP","math.SG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2025-02-10T19:00:03Z","title_canon_sha256":"c83cf6e813d0d22b6021221ca8935e07e27413826f69070e51f0e53d17a6a7d7"},"schema_version":"1.0","source":{"id":"2502.06951","kind":"arxiv","version":4}},"canonical_sha256":"7d752cbe773daa97b437eff2e5a3e2dd3872dc9a5d91156c2c03eebd014bb23b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d752cbe773daa97b437eff2e5a3e2dd3872dc9a5d91156c2c03eebd014bb23b","first_computed_at":"2026-07-05T12:11:15.487071Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:11:15.487071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JECgT/gTBw6ucscLyLGzSzKnMeBrxFN+Pc4xeU70Lf7du0QBt48rb5dOhXQOGJMw8qSEBsJanFn/LL/e/cogBA==","signature_status":"signed_v1","signed_at":"2026-07-05T12:11:15.487713Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.06951","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d076bce6156ad46faacb1080e92b1f3fedfa51cf7ef45022333d6c426e19ed7c","sha256:0f158f2891af34c0dda8d97d83007ecacea3a1f3d063f69b759aec665d3a1ff1"],"state_sha256":"2042c04bc68adb05b651ff465f6e84fe6f729c086e10c482c5da76208ff24f6f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F4wAxrbNs5tiNqfY/YVJlqz8rlVMfEqwX7cykbzupmBpzyXgn/5oe0J+aJI1JNa2YBm3rZQ6EA26hMlHoW1qCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T18:59:15.165163Z","bundle_sha256":"5881ec81ef1de819b209f14ff3b0eaa2b17f0d825e6cf9efe86fa37d8e74576c"}}