{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:JGCIURPYV23BXUICGTAAMMX5SU","short_pith_number":"pith:JGCIURPY","canonical_record":{"source":{"id":"2110.05504","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-10-11T18:00:04Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"8e27d9ac0441d5cdce72fa058d51a910b2605022acf4dfdf2431c3ce025f6b53","abstract_canon_sha256":"fdf400bdc5bbccd487a89ec89c3f49f19e73514c572cd10d79aaeed7a6a28263"},"schema_version":"1.0"},"canonical_sha256":"49848a45f8aeb61bd10234c00632fd952d464586fb8f9b0ed3d48c07cf794e3d","source":{"kind":"arxiv","id":"2110.05504","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.05504","created_at":"2026-07-05T04:03:53Z"},{"alias_kind":"arxiv_version","alias_value":"2110.05504v1","created_at":"2026-07-05T04:03:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.05504","created_at":"2026-07-05T04:03:53Z"},{"alias_kind":"pith_short_12","alias_value":"JGCIURPYV23B","created_at":"2026-07-05T04:03:53Z"},{"alias_kind":"pith_short_16","alias_value":"JGCIURPYV23BXUIC","created_at":"2026-07-05T04:03:53Z"},{"alias_kind":"pith_short_8","alias_value":"JGCIURPY","created_at":"2026-07-05T04:03:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:JGCIURPYV23BXUICGTAAMMX5SU","target":"record","payload":{"canonical_record":{"source":{"id":"2110.05504","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-10-11T18:00:04Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"8e27d9ac0441d5cdce72fa058d51a910b2605022acf4dfdf2431c3ce025f6b53","abstract_canon_sha256":"fdf400bdc5bbccd487a89ec89c3f49f19e73514c572cd10d79aaeed7a6a28263"},"schema_version":"1.0"},"canonical_sha256":"49848a45f8aeb61bd10234c00632fd952d464586fb8f9b0ed3d48c07cf794e3d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:03:53.563768Z","signature_b64":"AZ0O9uopRCjrc9Pm6mHelP5n4HzRzixD+C19r90reGHNv0c1Dw0LBOxURPGhZ3aV5RZb2Y0qNIMlC4dwKebOCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"49848a45f8aeb61bd10234c00632fd952d464586fb8f9b0ed3d48c07cf794e3d","last_reissued_at":"2026-07-05T04:03:53.563302Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:03:53.563302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2110.05504","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":"2026-07-05T04:03:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WYOQI4OHIm9j1Bdn0eYYa0OwwIREEpkEPticsKh4b6+DnCB0ufYpHMflsYlvKTcHf2TWBr32hztm+oZ4VF5cCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T10:33:50.114396Z"},"content_sha256":"9ce38784f756f64d2d7d9331ccec00399eb90e0f6d00634a7f1784eaf7480201","schema_version":"1.0","event_id":"sha256:9ce38784f756f64d2d7d9331ccec00399eb90e0f6d00634a7f1784eaf7480201"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:JGCIURPYV23BXUICGTAAMMX5SU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Scaling Black Holes and Modularity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"hep-th","authors_text":"Aradhita Chattopadhyaya, Jan Manschot, Swapnamay Mondal","submitted_at":"2021-10-11T18:00:04Z","abstract_excerpt":"Scaling black holes are solutions of supergravity with multiple black hole singularities, which can be adiabatically connected to a single center black hole solution. We develop techniques to determine partition functions for such scaling black holes, if each constituent carries a non-vanishing magnetic charge corresponding to a D4-brane in string theory, or equivalently M5-brane in M-theory. For three constituents, we demonstrate that the partition function is a mock modular form of depth two, and we determine the appropriate non-holomorphic completion using generalized error functions. From "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.05504","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/2110.05504/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":"2026-07-05T04:03:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qy+dNxSfU/T1ac1lEASFrvej2FE8AU5athYtMPkcJCdUPnaQifHNf6K6H827/0pFQs1Pq5yHOi0GKZhCGz14Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T10:33:50.114909Z"},"content_sha256":"b20dd10a37071d6c1f21d143736e977e320b640e580a68975fa7f2c85b96d37e","schema_version":"1.0","event_id":"sha256:b20dd10a37071d6c1f21d143736e977e320b640e580a68975fa7f2c85b96d37e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JGCIURPYV23BXUICGTAAMMX5SU/bundle.json","state_url":"https://pith.science/pith/JGCIURPYV23BXUICGTAAMMX5SU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JGCIURPYV23BXUICGTAAMMX5SU/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":"2026-08-05T10:33:50Z","links":{"resolver":"https://pith.science/pith/JGCIURPYV23BXUICGTAAMMX5SU","bundle":"https://pith.science/pith/JGCIURPYV23BXUICGTAAMMX5SU/bundle.json","state":"https://pith.science/pith/JGCIURPYV23BXUICGTAAMMX5SU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JGCIURPYV23BXUICGTAAMMX5SU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:JGCIURPYV23BXUICGTAAMMX5SU","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":"fdf400bdc5bbccd487a89ec89c3f49f19e73514c572cd10d79aaeed7a6a28263","cross_cats_sorted":["math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-10-11T18:00:04Z","title_canon_sha256":"8e27d9ac0441d5cdce72fa058d51a910b2605022acf4dfdf2431c3ce025f6b53"},"schema_version":"1.0","source":{"id":"2110.05504","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.05504","created_at":"2026-07-05T04:03:53Z"},{"alias_kind":"arxiv_version","alias_value":"2110.05504v1","created_at":"2026-07-05T04:03:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.05504","created_at":"2026-07-05T04:03:53Z"},{"alias_kind":"pith_short_12","alias_value":"JGCIURPYV23B","created_at":"2026-07-05T04:03:53Z"},{"alias_kind":"pith_short_16","alias_value":"JGCIURPYV23BXUIC","created_at":"2026-07-05T04:03:53Z"},{"alias_kind":"pith_short_8","alias_value":"JGCIURPY","created_at":"2026-07-05T04:03:53Z"}],"graph_snapshots":[{"event_id":"sha256:b20dd10a37071d6c1f21d143736e977e320b640e580a68975fa7f2c85b96d37e","target":"graph","created_at":"2026-07-05T04:03:53Z","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/2110.05504/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Scaling black holes are solutions of supergravity with multiple black hole singularities, which can be adiabatically connected to a single center black hole solution. We develop techniques to determine partition functions for such scaling black holes, if each constituent carries a non-vanishing magnetic charge corresponding to a D4-brane in string theory, or equivalently M5-brane in M-theory. For three constituents, we demonstrate that the partition function is a mock modular form of depth two, and we determine the appropriate non-holomorphic completion using generalized error functions. From ","authors_text":"Aradhita Chattopadhyaya, Jan Manschot, Swapnamay Mondal","cross_cats":["math.NT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-10-11T18:00:04Z","title":"Scaling Black Holes and Modularity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.05504","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":"sha256:9ce38784f756f64d2d7d9331ccec00399eb90e0f6d00634a7f1784eaf7480201","target":"record","created_at":"2026-07-05T04:03:53Z","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":"fdf400bdc5bbccd487a89ec89c3f49f19e73514c572cd10d79aaeed7a6a28263","cross_cats_sorted":["math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-10-11T18:00:04Z","title_canon_sha256":"8e27d9ac0441d5cdce72fa058d51a910b2605022acf4dfdf2431c3ce025f6b53"},"schema_version":"1.0","source":{"id":"2110.05504","kind":"arxiv","version":1}},"canonical_sha256":"49848a45f8aeb61bd10234c00632fd952d464586fb8f9b0ed3d48c07cf794e3d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"49848a45f8aeb61bd10234c00632fd952d464586fb8f9b0ed3d48c07cf794e3d","first_computed_at":"2026-07-05T04:03:53.563302Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:03:53.563302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AZ0O9uopRCjrc9Pm6mHelP5n4HzRzixD+C19r90reGHNv0c1Dw0LBOxURPGhZ3aV5RZb2Y0qNIMlC4dwKebOCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:03:53.563768Z","signed_message":"canonical_sha256_bytes"},"source_id":"2110.05504","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ce38784f756f64d2d7d9331ccec00399eb90e0f6d00634a7f1784eaf7480201","sha256:b20dd10a37071d6c1f21d143736e977e320b640e580a68975fa7f2c85b96d37e"],"state_sha256":"4e9abc098eafa77085b7c8f2b60b494f873a5243eb20eb12de2463ad02b520d3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GMeu6oUCnOz09syQs2C72dMZyC9kz5DVZuOLcxHtAba2P2e31t57qtc23r0kTrz1hlmhYfhNAmr7qpa2nnp6CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T10:33:50.118787Z","bundle_sha256":"dac420da7d4fc0732e7cb0ade666c91e9233f3d26c4aaba5f5d24a8112060ad8"}}