{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:4QUNYF3VZFQQRJYNWLZH3F5OXA","short_pith_number":"pith:4QUNYF3V","canonical_record":{"source":{"id":"2606.28298","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2026-06-26T17:41:03Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"6a039b9225e8284a46aaf96047760f99380ba701f6e3bec2c92940fb07e3eb59","abstract_canon_sha256":"fb13e6158fd858b8546fabd40d9225d6c67e6454358dd33ebf543b57071e6682"},"schema_version":"1.0"},"canonical_sha256":"e428dc1775c96108a70db2f27d97aeb83ad28a683fa5a04750d92f8097a59777","source":{"kind":"arxiv","id":"2606.28298","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.28298","created_at":"2026-06-29T01:15:12Z"},{"alias_kind":"arxiv_version","alias_value":"2606.28298v1","created_at":"2026-06-29T01:15:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.28298","created_at":"2026-06-29T01:15:12Z"},{"alias_kind":"pith_short_12","alias_value":"4QUNYF3VZFQQ","created_at":"2026-06-29T01:15:12Z"},{"alias_kind":"pith_short_16","alias_value":"4QUNYF3VZFQQRJYN","created_at":"2026-06-29T01:15:12Z"},{"alias_kind":"pith_short_8","alias_value":"4QUNYF3V","created_at":"2026-06-29T01:15:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:4QUNYF3VZFQQRJYNWLZH3F5OXA","target":"record","payload":{"canonical_record":{"source":{"id":"2606.28298","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2026-06-26T17:41:03Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"6a039b9225e8284a46aaf96047760f99380ba701f6e3bec2c92940fb07e3eb59","abstract_canon_sha256":"fb13e6158fd858b8546fabd40d9225d6c67e6454358dd33ebf543b57071e6682"},"schema_version":"1.0"},"canonical_sha256":"e428dc1775c96108a70db2f27d97aeb83ad28a683fa5a04750d92f8097a59777","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-29T01:15:12.367547Z","signature_b64":"M2wfHVVN0+xeHxQfXVrHE/RgTIH0oOu0HeKiKSal+202s8qTTHS+4WnjJanSeXQ6EW610jPFXN8k07Fly4X7AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e428dc1775c96108a70db2f27d97aeb83ad28a683fa5a04750d92f8097a59777","last_reissued_at":"2026-06-29T01:15:12.367155Z","signature_status":"signed_v1","first_computed_at":"2026-06-29T01:15:12.367155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.28298","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":"2026-06-29T01:15:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PrLHIGIPxh7uZRg6n1tqgz8fJs73pK6UpQztCQSDRnY3UPbxRT9uR3014F9Dxf8zUUa11ofQZTV0XQfIrjVtDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T20:59:00.047441Z"},"content_sha256":"81ca003883e38d644477826e93d45d06bacb09798e2d992b7a4ae5d9ba2ab14c","schema_version":"1.0","event_id":"sha256:81ca003883e38d644477826e93d45d06bacb09798e2d992b7a4ae5d9ba2ab14c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:4QUNYF3VZFQQRJYNWLZH3F5OXA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stationary point complexity via minimal supersymmetry breaking","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cond-mat.dis-nn","authors_text":"Jaron Kent-Dobias","submitted_at":"2026-06-26T17:41:03Z","abstract_excerpt":"The statistics of stationary points are a powerful way to understand mean-field random landscapes, and the Kac--Rice formula is a general way to compute them. A longstanding technical barrier to these calculations is the presence of the absolute value of the determinant of the Hessian. Neglecting the absolute value produces an elegant 2-index supersymmetric representation of the problem, but is often incorrect. We develop an expanded 4-index supersymmetric representation of the complexity problem which incorporates the absolute value naturally via spontaneous supersymmetry breaking along a par"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.28298","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/2606.28298/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":"2026-06-29T01:15:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iJNTJYbJJhw9plU8eGJsjz9nfN/f7pSQeWROHI/USapJV94n1KY3FAJSdhQYgATT2/arPRTWsOCMxSyrYeFgAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T20:59:00.047823Z"},"content_sha256":"c6bf2e7ef081636d2c8c4573fb37d698e90d3629465d74cabf400d52e8ad6544","schema_version":"1.0","event_id":"sha256:c6bf2e7ef081636d2c8c4573fb37d698e90d3629465d74cabf400d52e8ad6544"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4QUNYF3VZFQQRJYNWLZH3F5OXA/bundle.json","state_url":"https://pith.science/pith/4QUNYF3VZFQQRJYNWLZH3F5OXA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4QUNYF3VZFQQRJYNWLZH3F5OXA/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":"2026-06-29T20:59:00Z","links":{"resolver":"https://pith.science/pith/4QUNYF3VZFQQRJYNWLZH3F5OXA","bundle":"https://pith.science/pith/4QUNYF3VZFQQRJYNWLZH3F5OXA/bundle.json","state":"https://pith.science/pith/4QUNYF3VZFQQRJYNWLZH3F5OXA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4QUNYF3VZFQQRJYNWLZH3F5OXA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:4QUNYF3VZFQQRJYNWLZH3F5OXA","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":"fb13e6158fd858b8546fabd40d9225d6c67e6454358dd33ebf543b57071e6682","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2026-06-26T17:41:03Z","title_canon_sha256":"6a039b9225e8284a46aaf96047760f99380ba701f6e3bec2c92940fb07e3eb59"},"schema_version":"1.0","source":{"id":"2606.28298","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.28298","created_at":"2026-06-29T01:15:12Z"},{"alias_kind":"arxiv_version","alias_value":"2606.28298v1","created_at":"2026-06-29T01:15:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.28298","created_at":"2026-06-29T01:15:12Z"},{"alias_kind":"pith_short_12","alias_value":"4QUNYF3VZFQQ","created_at":"2026-06-29T01:15:12Z"},{"alias_kind":"pith_short_16","alias_value":"4QUNYF3VZFQQRJYN","created_at":"2026-06-29T01:15:12Z"},{"alias_kind":"pith_short_8","alias_value":"4QUNYF3V","created_at":"2026-06-29T01:15:12Z"}],"graph_snapshots":[{"event_id":"sha256:c6bf2e7ef081636d2c8c4573fb37d698e90d3629465d74cabf400d52e8ad6544","target":"graph","created_at":"2026-06-29T01:15:12Z","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/2606.28298/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The statistics of stationary points are a powerful way to understand mean-field random landscapes, and the Kac--Rice formula is a general way to compute them. A longstanding technical barrier to these calculations is the presence of the absolute value of the determinant of the Hessian. Neglecting the absolute value produces an elegant 2-index supersymmetric representation of the problem, but is often incorrect. We develop an expanded 4-index supersymmetric representation of the complexity problem which incorporates the absolute value naturally via spontaneous supersymmetry breaking along a par","authors_text":"Jaron Kent-Dobias","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2026-06-26T17:41:03Z","title":"Stationary point complexity via minimal supersymmetry breaking"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.28298","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":"sha256:81ca003883e38d644477826e93d45d06bacb09798e2d992b7a4ae5d9ba2ab14c","target":"record","created_at":"2026-06-29T01:15:12Z","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":"fb13e6158fd858b8546fabd40d9225d6c67e6454358dd33ebf543b57071e6682","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2026-06-26T17:41:03Z","title_canon_sha256":"6a039b9225e8284a46aaf96047760f99380ba701f6e3bec2c92940fb07e3eb59"},"schema_version":"1.0","source":{"id":"2606.28298","kind":"arxiv","version":1}},"canonical_sha256":"e428dc1775c96108a70db2f27d97aeb83ad28a683fa5a04750d92f8097a59777","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e428dc1775c96108a70db2f27d97aeb83ad28a683fa5a04750d92f8097a59777","first_computed_at":"2026-06-29T01:15:12.367155Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-29T01:15:12.367155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M2wfHVVN0+xeHxQfXVrHE/RgTIH0oOu0HeKiKSal+202s8qTTHS+4WnjJanSeXQ6EW610jPFXN8k07Fly4X7AQ==","signature_status":"signed_v1","signed_at":"2026-06-29T01:15:12.367547Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.28298","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81ca003883e38d644477826e93d45d06bacb09798e2d992b7a4ae5d9ba2ab14c","sha256:c6bf2e7ef081636d2c8c4573fb37d698e90d3629465d74cabf400d52e8ad6544"],"state_sha256":"1af7040a020096a8d3fc377b7b496bf23d995d247c43921f48b65ae723eae652"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EE2ZZ8pbEvA0E7ogweAYhvn0pbBfC2RQQRgC/AFIeQcX+Cw6SXsX71JIxScuIfk1wTMTqPs/sTqd4YsdTXrLDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T20:59:00.049782Z","bundle_sha256":"a61c9cf01f04686b602c51b051b16022c11fb4ab94821b9834fccc38e8bb5b31"}}