{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:EQUXM6SXHHNS4ZSPIQQZZHGVOH","short_pith_number":"pith:EQUXM6SX","canonical_record":{"source":{"id":"2506.09972","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2025-06-11T17:47:30Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"68af4586075472dd35a4c71a48381e4e5a73de707bc63ae40fa12e7688782019","abstract_canon_sha256":"8fa45afd7b8ca9f6d2d631a05eecb3a9bbbc3554917bbf313ac634fd8d8b333e"},"schema_version":"1.0"},"canonical_sha256":"2429767a5739db2e664f44219c9cd571c2a759c5078ad97df858eb0791e89224","source":{"kind":"arxiv","id":"2506.09972","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.09972","created_at":"2026-07-05T11:48:49Z"},{"alias_kind":"arxiv_version","alias_value":"2506.09972v2","created_at":"2026-07-05T11:48:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.09972","created_at":"2026-07-05T11:48:49Z"},{"alias_kind":"pith_short_12","alias_value":"EQUXM6SXHHNS","created_at":"2026-07-05T11:48:49Z"},{"alias_kind":"pith_short_16","alias_value":"EQUXM6SXHHNS4ZSP","created_at":"2026-07-05T11:48:49Z"},{"alias_kind":"pith_short_8","alias_value":"EQUXM6SX","created_at":"2026-07-05T11:48:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:EQUXM6SXHHNS4ZSPIQQZZHGVOH","target":"record","payload":{"canonical_record":{"source":{"id":"2506.09972","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2025-06-11T17:47:30Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"68af4586075472dd35a4c71a48381e4e5a73de707bc63ae40fa12e7688782019","abstract_canon_sha256":"8fa45afd7b8ca9f6d2d631a05eecb3a9bbbc3554917bbf313ac634fd8d8b333e"},"schema_version":"1.0"},"canonical_sha256":"2429767a5739db2e664f44219c9cd571c2a759c5078ad97df858eb0791e89224","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:48:49.852293Z","signature_b64":"rPtgjj360SYRsNo1207wAxCxQ3mp0JJoyB72gm+NVE7/lIjQNgx9/zbezsAkd27JAILDjZlKf/HC3c/w6jbjAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2429767a5739db2e664f44219c9cd571c2a759c5078ad97df858eb0791e89224","last_reissued_at":"2026-07-05T11:48:49.851824Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:48:49.851824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.09972","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":"2026-07-05T11:48:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A2HvgAkHDzdbA8kTuxvwSwY5SLGgkiS49taHWPFsZ/up5Sx9cy2ks82q94h+wKhxn4pZfUTjE2IUeuwV5gVvDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T06:53:04.192133Z"},"content_sha256":"0bd3e798114f35bbfa530147061a86bd1204535a42210096a7dee3120875f0e7","schema_version":"1.0","event_id":"sha256:0bd3e798114f35bbfa530147061a86bd1204535a42210096a7dee3120875f0e7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:EQUXM6SXHHNS4ZSPIQQZZHGVOH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Wild wall-crossing and symmetric quivers in 4d and 3d $\\mathcal{N}=2$ field theories","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Daniel Bryan, Piotr Su{\\l}kowski","submitted_at":"2025-06-11T17:47:30Z","abstract_excerpt":"We reformulate Kontsevich-Soibelman wall-crossing formulae for 4d $\\mathcal{N}=2$ class $\\mathcal{S}$ theories and corresponding BPS quivers, including those of wild type, as identities for generating series of symmetric quivers that represent dualities of 3d $\\mathcal{N}=2$ boundary theories. We identify such symmetric quivers for both sides of the wall-crossing formulae. In the finite chamber such a quiver is captured by the symmetrized BPS quiver, whereas on the other side of the wall we find an infinite quiver with an intricate pattern of arrows and loops. Invoking diagonalization, for $m$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.09972","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/2506.09972/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":"2026-07-05T11:48:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YDQ74hPa1psvERF1qVSKpUkOqiCfYY9ng+24fLciacjUc1D+uyFThY9Pk4udjsutj6C0Ow424F4JARERBVYXBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T06:53:04.192489Z"},"content_sha256":"39045c79f543f03390dead641b1b6e63a3a0dd1ec265054439c383acc8f21e3f","schema_version":"1.0","event_id":"sha256:39045c79f543f03390dead641b1b6e63a3a0dd1ec265054439c383acc8f21e3f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EQUXM6SXHHNS4ZSPIQQZZHGVOH/bundle.json","state_url":"https://pith.science/pith/EQUXM6SXHHNS4ZSPIQQZZHGVOH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EQUXM6SXHHNS4ZSPIQQZZHGVOH/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":"2026-08-20T06:53:04Z","links":{"resolver":"https://pith.science/pith/EQUXM6SXHHNS4ZSPIQQZZHGVOH","bundle":"https://pith.science/pith/EQUXM6SXHHNS4ZSPIQQZZHGVOH/bundle.json","state":"https://pith.science/pith/EQUXM6SXHHNS4ZSPIQQZZHGVOH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EQUXM6SXHHNS4ZSPIQQZZHGVOH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:EQUXM6SXHHNS4ZSPIQQZZHGVOH","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":"8fa45afd7b8ca9f6d2d631a05eecb3a9bbbc3554917bbf313ac634fd8d8b333e","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2025-06-11T17:47:30Z","title_canon_sha256":"68af4586075472dd35a4c71a48381e4e5a73de707bc63ae40fa12e7688782019"},"schema_version":"1.0","source":{"id":"2506.09972","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.09972","created_at":"2026-07-05T11:48:49Z"},{"alias_kind":"arxiv_version","alias_value":"2506.09972v2","created_at":"2026-07-05T11:48:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.09972","created_at":"2026-07-05T11:48:49Z"},{"alias_kind":"pith_short_12","alias_value":"EQUXM6SXHHNS","created_at":"2026-07-05T11:48:49Z"},{"alias_kind":"pith_short_16","alias_value":"EQUXM6SXHHNS4ZSP","created_at":"2026-07-05T11:48:49Z"},{"alias_kind":"pith_short_8","alias_value":"EQUXM6SX","created_at":"2026-07-05T11:48:49Z"}],"graph_snapshots":[{"event_id":"sha256:39045c79f543f03390dead641b1b6e63a3a0dd1ec265054439c383acc8f21e3f","target":"graph","created_at":"2026-07-05T11:48:49Z","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/2506.09972/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We reformulate Kontsevich-Soibelman wall-crossing formulae for 4d $\\mathcal{N}=2$ class $\\mathcal{S}$ theories and corresponding BPS quivers, including those of wild type, as identities for generating series of symmetric quivers that represent dualities of 3d $\\mathcal{N}=2$ boundary theories. We identify such symmetric quivers for both sides of the wall-crossing formulae. In the finite chamber such a quiver is captured by the symmetrized BPS quiver, whereas on the other side of the wall we find an infinite quiver with an intricate pattern of arrows and loops. Invoking diagonalization, for $m$","authors_text":"Daniel Bryan, Piotr Su{\\l}kowski","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2025-06-11T17:47:30Z","title":"Wild wall-crossing and symmetric quivers in 4d and 3d $\\mathcal{N}=2$ field theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.09972","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":"sha256:0bd3e798114f35bbfa530147061a86bd1204535a42210096a7dee3120875f0e7","target":"record","created_at":"2026-07-05T11:48:49Z","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":"8fa45afd7b8ca9f6d2d631a05eecb3a9bbbc3554917bbf313ac634fd8d8b333e","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2025-06-11T17:47:30Z","title_canon_sha256":"68af4586075472dd35a4c71a48381e4e5a73de707bc63ae40fa12e7688782019"},"schema_version":"1.0","source":{"id":"2506.09972","kind":"arxiv","version":2}},"canonical_sha256":"2429767a5739db2e664f44219c9cd571c2a759c5078ad97df858eb0791e89224","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2429767a5739db2e664f44219c9cd571c2a759c5078ad97df858eb0791e89224","first_computed_at":"2026-07-05T11:48:49.851824Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:48:49.851824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rPtgjj360SYRsNo1207wAxCxQ3mp0JJoyB72gm+NVE7/lIjQNgx9/zbezsAkd27JAILDjZlKf/HC3c/w6jbjAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:48:49.852293Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.09972","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0bd3e798114f35bbfa530147061a86bd1204535a42210096a7dee3120875f0e7","sha256:39045c79f543f03390dead641b1b6e63a3a0dd1ec265054439c383acc8f21e3f"],"state_sha256":"9a0f9ecd04aa2c8edaf452eb98526e313183c422905a0a2246ae33e5e22d3037"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mXKTapvg4TmGOfw5yKfdK2g5z6Fohg8RT3dYN4zJHfOaNJG4Gnadxvc1t3QCxfbRpBdDMYGxs/rXAIBDOzImCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T06:53:04.196219Z","bundle_sha256":"d3bd99717699009a5fb68eedecc08da39d9adb43710d926100cfd55d4acec065"}}