{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:2MZNRI3ZKNLYBWCJW7LI2TGBEP","short_pith_number":"pith:2MZNRI3Z","canonical_record":{"source":{"id":"2606.02805","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-06-01T19:24:49Z","cross_cats_sorted":["cs.DS","math.AG","math.RT"],"title_canon_sha256":"ae7fdf8af3c703c1e11659173b55cfffcf7ba7e4863a4e77ca6f672336d7982c","abstract_canon_sha256":"0783f48bd5b4579567871ffdd2ede9951f9f57582aa3ddb901a7a0fc923650ec"},"schema_version":"1.0"},"canonical_sha256":"d332d8a379535780d849b7d68d4cc123e35456a2af8d53cded616854cfcac7d1","source":{"kind":"arxiv","id":"2606.02805","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.02805","created_at":"2026-06-03T01:05:23Z"},{"alias_kind":"arxiv_version","alias_value":"2606.02805v1","created_at":"2026-06-03T01:05:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.02805","created_at":"2026-06-03T01:05:23Z"},{"alias_kind":"pith_short_12","alias_value":"2MZNRI3ZKNLY","created_at":"2026-06-03T01:05:23Z"},{"alias_kind":"pith_short_16","alias_value":"2MZNRI3ZKNLYBWCJ","created_at":"2026-06-03T01:05:23Z"},{"alias_kind":"pith_short_8","alias_value":"2MZNRI3Z","created_at":"2026-06-03T01:05:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:2MZNRI3ZKNLYBWCJW7LI2TGBEP","target":"record","payload":{"canonical_record":{"source":{"id":"2606.02805","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-06-01T19:24:49Z","cross_cats_sorted":["cs.DS","math.AG","math.RT"],"title_canon_sha256":"ae7fdf8af3c703c1e11659173b55cfffcf7ba7e4863a4e77ca6f672336d7982c","abstract_canon_sha256":"0783f48bd5b4579567871ffdd2ede9951f9f57582aa3ddb901a7a0fc923650ec"},"schema_version":"1.0"},"canonical_sha256":"d332d8a379535780d849b7d68d4cc123e35456a2af8d53cded616854cfcac7d1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T01:05:23.487795Z","signature_b64":"YYn1WrXJp7XL7dvvjE4G3o2elMQ/Liaxmnp+4hv56TX5PiRkTol/BDjUIoEmhEL17WnXGEtBP4DIMwuYV6RsBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d332d8a379535780d849b7d68d4cc123e35456a2af8d53cded616854cfcac7d1","last_reissued_at":"2026-06-03T01:05:23.487426Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T01:05:23.487426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.02805","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":"2026-06-03T01:05:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/Xp0GChMP2zvLERDUSOZFyLn58TjHIRTHTFaxziPry7IIr49CLLH4UOG86doziVTaUgKiO9R637OGS+LvfXuBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T03:39:55.130916Z"},"content_sha256":"bb02c964f4ee1f58155828450edf07017aee3bc909a2dffc61fbadf5a15da89d","schema_version":"1.0","event_id":"sha256:bb02c964f4ee1f58155828450edf07017aee3bc909a2dffc61fbadf5a15da89d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:2MZNRI3ZKNLYBWCJW7LI2TGBEP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the gap of quiver representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.AG","math.RT"],"primary_cat":"math.OC","authors_text":"John Maar","submitted_at":"2026-06-01T19:24:49Z","abstract_excerpt":"The nullcone membership problem, deciding whether an orbit closure contains the origin, is fundamental in computational invariant theory. For self-adjoint groups, B\\\"urgisser, Franks, Garg, Oliveira, Walter and Wigderson gave a geodesic optimization algorithm whose complexity is controlled by the gap, a condition number of the representation. We study the gap for quiver representations under the action of the special linear group.\n  We prove that the inverse gap is polynomially bounded in the number of vertices and the maximum dimension for type A and $\\hat{A}$, as well as tree quivers with un"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.02805","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/2606.02805/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":"2026-06-03T01:05:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JbWCwzJSGTXyy3UN/kSNVVd7esTHZsRepTPGcqwOE9A64120BrbInfpQz0DR+jYV82JZvUOt/ZUB9gNipHQGCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T03:39:55.131284Z"},"content_sha256":"26a0e734b397b86c7510911530c2f5840c2204ed6376d95eb0024ca980d2fca3","schema_version":"1.0","event_id":"sha256:26a0e734b397b86c7510911530c2f5840c2204ed6376d95eb0024ca980d2fca3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2MZNRI3ZKNLYBWCJW7LI2TGBEP/bundle.json","state_url":"https://pith.science/pith/2MZNRI3ZKNLYBWCJW7LI2TGBEP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2MZNRI3ZKNLYBWCJW7LI2TGBEP/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":"2026-06-30T03:39:55Z","links":{"resolver":"https://pith.science/pith/2MZNRI3ZKNLYBWCJW7LI2TGBEP","bundle":"https://pith.science/pith/2MZNRI3ZKNLYBWCJW7LI2TGBEP/bundle.json","state":"https://pith.science/pith/2MZNRI3ZKNLYBWCJW7LI2TGBEP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2MZNRI3ZKNLYBWCJW7LI2TGBEP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:2MZNRI3ZKNLYBWCJW7LI2TGBEP","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":"0783f48bd5b4579567871ffdd2ede9951f9f57582aa3ddb901a7a0fc923650ec","cross_cats_sorted":["cs.DS","math.AG","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-06-01T19:24:49Z","title_canon_sha256":"ae7fdf8af3c703c1e11659173b55cfffcf7ba7e4863a4e77ca6f672336d7982c"},"schema_version":"1.0","source":{"id":"2606.02805","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.02805","created_at":"2026-06-03T01:05:23Z"},{"alias_kind":"arxiv_version","alias_value":"2606.02805v1","created_at":"2026-06-03T01:05:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.02805","created_at":"2026-06-03T01:05:23Z"},{"alias_kind":"pith_short_12","alias_value":"2MZNRI3ZKNLY","created_at":"2026-06-03T01:05:23Z"},{"alias_kind":"pith_short_16","alias_value":"2MZNRI3ZKNLYBWCJ","created_at":"2026-06-03T01:05:23Z"},{"alias_kind":"pith_short_8","alias_value":"2MZNRI3Z","created_at":"2026-06-03T01:05:23Z"}],"graph_snapshots":[{"event_id":"sha256:26a0e734b397b86c7510911530c2f5840c2204ed6376d95eb0024ca980d2fca3","target":"graph","created_at":"2026-06-03T01:05:23Z","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/2606.02805/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The nullcone membership problem, deciding whether an orbit closure contains the origin, is fundamental in computational invariant theory. For self-adjoint groups, B\\\"urgisser, Franks, Garg, Oliveira, Walter and Wigderson gave a geodesic optimization algorithm whose complexity is controlled by the gap, a condition number of the representation. We study the gap for quiver representations under the action of the special linear group.\n  We prove that the inverse gap is polynomially bounded in the number of vertices and the maximum dimension for type A and $\\hat{A}$, as well as tree quivers with un","authors_text":"John Maar","cross_cats":["cs.DS","math.AG","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-06-01T19:24:49Z","title":"On the gap of quiver representations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.02805","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:bb02c964f4ee1f58155828450edf07017aee3bc909a2dffc61fbadf5a15da89d","target":"record","created_at":"2026-06-03T01:05:23Z","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":"0783f48bd5b4579567871ffdd2ede9951f9f57582aa3ddb901a7a0fc923650ec","cross_cats_sorted":["cs.DS","math.AG","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-06-01T19:24:49Z","title_canon_sha256":"ae7fdf8af3c703c1e11659173b55cfffcf7ba7e4863a4e77ca6f672336d7982c"},"schema_version":"1.0","source":{"id":"2606.02805","kind":"arxiv","version":1}},"canonical_sha256":"d332d8a379535780d849b7d68d4cc123e35456a2af8d53cded616854cfcac7d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d332d8a379535780d849b7d68d4cc123e35456a2af8d53cded616854cfcac7d1","first_computed_at":"2026-06-03T01:05:23.487426Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T01:05:23.487426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YYn1WrXJp7XL7dvvjE4G3o2elMQ/Liaxmnp+4hv56TX5PiRkTol/BDjUIoEmhEL17WnXGEtBP4DIMwuYV6RsBw==","signature_status":"signed_v1","signed_at":"2026-06-03T01:05:23.487795Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.02805","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb02c964f4ee1f58155828450edf07017aee3bc909a2dffc61fbadf5a15da89d","sha256:26a0e734b397b86c7510911530c2f5840c2204ed6376d95eb0024ca980d2fca3"],"state_sha256":"0a6a4d80ca0514fb99f9d866658711765393034c6350c91ba4109589ab1ccd0e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Cb0mCeieJtz/kxc3MkrIADK1LLMl34/VPB9wl87z+KfXN95RFfLZLDcKG2Z7AiOxBp2nVWEJzE2lDALuaxjeBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T03:39:55.133179Z","bundle_sha256":"96ea6f0b3d5b46a945ceb15948caebf624ad0b1aad787f5b7cbb72b451dd62cf"}}