{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:V3722RWVGQEMWRHXE6HATBZW4D","short_pith_number":"pith:V3722RWV","canonical_record":{"source":{"id":"2505.02572","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-05-05T11:22:03Z","cross_cats_sorted":["gr-qc","math-ph","math.AG","math.MP","math.NT"],"title_canon_sha256":"090227eab9422e82177d430240d6e8f265c81ba96bf0079e857654f07e58ddbd","abstract_canon_sha256":"6d9b46ff3deb240ea64d279cbf83a8e1719010c28d8fd65a2ba38236ee18b6ed"},"schema_version":"1.0"},"canonical_sha256":"aeffad46d53408cb44f7278e098736e0daff149621601140c3452efad8a7a0d0","source":{"kind":"arxiv","id":"2505.02572","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.02572","created_at":"2026-07-05T11:35:13Z"},{"alias_kind":"arxiv_version","alias_value":"2505.02572v2","created_at":"2026-07-05T11:35:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.02572","created_at":"2026-07-05T11:35:13Z"},{"alias_kind":"pith_short_12","alias_value":"V3722RWVGQEM","created_at":"2026-07-05T11:35:13Z"},{"alias_kind":"pith_short_16","alias_value":"V3722RWVGQEMWRHX","created_at":"2026-07-05T11:35:13Z"},{"alias_kind":"pith_short_8","alias_value":"V3722RWV","created_at":"2026-07-05T11:35:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:V3722RWVGQEMWRHXE6HATBZW4D","target":"record","payload":{"canonical_record":{"source":{"id":"2505.02572","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-05-05T11:22:03Z","cross_cats_sorted":["gr-qc","math-ph","math.AG","math.MP","math.NT"],"title_canon_sha256":"090227eab9422e82177d430240d6e8f265c81ba96bf0079e857654f07e58ddbd","abstract_canon_sha256":"6d9b46ff3deb240ea64d279cbf83a8e1719010c28d8fd65a2ba38236ee18b6ed"},"schema_version":"1.0"},"canonical_sha256":"aeffad46d53408cb44f7278e098736e0daff149621601140c3452efad8a7a0d0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:35:13.473019Z","signature_b64":"jO327Z3gywwBXTw8UGadRbW9oqp2s10qlOKhRoIUvdH8PG/jD6wdRDHLmOh1TR19HB/AH9Ic2FAU7k2oEjwuBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aeffad46d53408cb44f7278e098736e0daff149621601140c3452efad8a7a0d0","last_reissued_at":"2026-07-05T11:35:13.472500Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:35:13.472500Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.02572","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":"2026-07-05T11:35:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iCFFh/d1dGDLMij128R6NRE+taIURUdIUQ247mBogfQfq73XJPY64IjOtpPZWE6NB4/v69tJG6d9CfaX9KjsAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T17:24:52.097793Z"},"content_sha256":"7a73f638b42bc4e31f928ebac6930d4ccc8f6f4a7cba3f27c2e9a0bebc1839b4","schema_version":"1.0","event_id":"sha256:7a73f638b42bc4e31f928ebac6930d4ccc8f6f4a7cba3f27c2e9a0bebc1839b4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:V3722RWVGQEMWRHXE6HATBZW4D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mock modularity at work, or black holes in a forest","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math-ph","math.AG","math.MP","math.NT"],"primary_cat":"hep-th","authors_text":"Sergei Alexandrov","submitted_at":"2025-05-05T11:22:03Z","abstract_excerpt":"Mock modular forms, first invented by Ramanujan, provide a beautiful generalization of the usual modular forms. In recent years, it was found that they capture generating functions of the number of microstates of BPS black holes appearing in compactifications of string theory with 8 and 16 supercharges. This review describes these results and their applications which range from the actual computation of these generating functions for both compact and non-compact compactification manifolds (encoding, respectively, Donaldson-Thomas and Vafa-Witten topological invariants) to the construction of n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.02572","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.02572/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":"2026-07-05T11:35:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dkYnZwVMaSc/Lkk2x4j+FeVHQ6XJOIttfRz3hZF2qq+lm+9BFQYgK51Vta7es4AT8rXQOs66K6kXGtAD+IMyCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T17:24:52.099702Z"},"content_sha256":"7c4e1b3d4dc2af345a5e538375ab0b20e911961a81ae597efd5fecafd3e8df59","schema_version":"1.0","event_id":"sha256:7c4e1b3d4dc2af345a5e538375ab0b20e911961a81ae597efd5fecafd3e8df59"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V3722RWVGQEMWRHXE6HATBZW4D/bundle.json","state_url":"https://pith.science/pith/V3722RWVGQEMWRHXE6HATBZW4D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V3722RWVGQEMWRHXE6HATBZW4D/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":"2026-08-04T17:24:52Z","links":{"resolver":"https://pith.science/pith/V3722RWVGQEMWRHXE6HATBZW4D","bundle":"https://pith.science/pith/V3722RWVGQEMWRHXE6HATBZW4D/bundle.json","state":"https://pith.science/pith/V3722RWVGQEMWRHXE6HATBZW4D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V3722RWVGQEMWRHXE6HATBZW4D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:V3722RWVGQEMWRHXE6HATBZW4D","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":"6d9b46ff3deb240ea64d279cbf83a8e1719010c28d8fd65a2ba38236ee18b6ed","cross_cats_sorted":["gr-qc","math-ph","math.AG","math.MP","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-05-05T11:22:03Z","title_canon_sha256":"090227eab9422e82177d430240d6e8f265c81ba96bf0079e857654f07e58ddbd"},"schema_version":"1.0","source":{"id":"2505.02572","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.02572","created_at":"2026-07-05T11:35:13Z"},{"alias_kind":"arxiv_version","alias_value":"2505.02572v2","created_at":"2026-07-05T11:35:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.02572","created_at":"2026-07-05T11:35:13Z"},{"alias_kind":"pith_short_12","alias_value":"V3722RWVGQEM","created_at":"2026-07-05T11:35:13Z"},{"alias_kind":"pith_short_16","alias_value":"V3722RWVGQEMWRHX","created_at":"2026-07-05T11:35:13Z"},{"alias_kind":"pith_short_8","alias_value":"V3722RWV","created_at":"2026-07-05T11:35:13Z"}],"graph_snapshots":[{"event_id":"sha256:7c4e1b3d4dc2af345a5e538375ab0b20e911961a81ae597efd5fecafd3e8df59","target":"graph","created_at":"2026-07-05T11:35:13Z","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/2505.02572/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Mock modular forms, first invented by Ramanujan, provide a beautiful generalization of the usual modular forms. In recent years, it was found that they capture generating functions of the number of microstates of BPS black holes appearing in compactifications of string theory with 8 and 16 supercharges. This review describes these results and their applications which range from the actual computation of these generating functions for both compact and non-compact compactification manifolds (encoding, respectively, Donaldson-Thomas and Vafa-Witten topological invariants) to the construction of n","authors_text":"Sergei Alexandrov","cross_cats":["gr-qc","math-ph","math.AG","math.MP","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-05-05T11:22:03Z","title":"Mock modularity at work, or black holes in a forest"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.02572","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":"sha256:7a73f638b42bc4e31f928ebac6930d4ccc8f6f4a7cba3f27c2e9a0bebc1839b4","target":"record","created_at":"2026-07-05T11:35:13Z","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":"6d9b46ff3deb240ea64d279cbf83a8e1719010c28d8fd65a2ba38236ee18b6ed","cross_cats_sorted":["gr-qc","math-ph","math.AG","math.MP","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-05-05T11:22:03Z","title_canon_sha256":"090227eab9422e82177d430240d6e8f265c81ba96bf0079e857654f07e58ddbd"},"schema_version":"1.0","source":{"id":"2505.02572","kind":"arxiv","version":2}},"canonical_sha256":"aeffad46d53408cb44f7278e098736e0daff149621601140c3452efad8a7a0d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aeffad46d53408cb44f7278e098736e0daff149621601140c3452efad8a7a0d0","first_computed_at":"2026-07-05T11:35:13.472500Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:35:13.472500Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jO327Z3gywwBXTw8UGadRbW9oqp2s10qlOKhRoIUvdH8PG/jD6wdRDHLmOh1TR19HB/AH9Ic2FAU7k2oEjwuBw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:35:13.473019Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.02572","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a73f638b42bc4e31f928ebac6930d4ccc8f6f4a7cba3f27c2e9a0bebc1839b4","sha256:7c4e1b3d4dc2af345a5e538375ab0b20e911961a81ae597efd5fecafd3e8df59"],"state_sha256":"ddd6df2b640e80d6d4a40085870aef931ab49833dedfdfb7c562b9fdd5d0b6cc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IimBCNEXY5wvcFSXpkRYGkRR8Wakg4T4v+gMnLT9hrXIhylEZ3seWF65o+NMbg4be8qacsqih/7nK8sJz+nOBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T17:24:52.111086Z","bundle_sha256":"6beb0e18918419589b7979e10ed8afb50fd9d6031be6c400c43fd45277a51613"}}