{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YA2STQLGXRHFD77PJ5AHGA3U74","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":"ac52f5119fd8872f8e65e1a86240adad58b3a67836ff3b268f7fc063d6821e34","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-23T09:50:14Z","title_canon_sha256":"cf535195dc44631b3cfb40312cf8e7d95a0492573f557560cc8f8daa0c6c841e"},"schema_version":"1.0","source":{"id":"1511.07157","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.07157","created_at":"2026-05-18T01:26:12Z"},{"alias_kind":"arxiv_version","alias_value":"1511.07157v1","created_at":"2026-05-18T01:26:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.07157","created_at":"2026-05-18T01:26:12Z"},{"alias_kind":"pith_short_12","alias_value":"YA2STQLGXRHF","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"YA2STQLGXRHFD77P","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"YA2STQLG","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:1461e0afba8e5e6b847605fcdf809997faf24c2a64bc40f3b83ead57489b55db","target":"graph","created_at":"2026-05-18T01:26:12Z","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"},"paper":{"abstract_excerpt":"Sabot and Zeng have discovered two martingales, one of which played a key role in their investigation of the vertex-reinforced jump process. Starting from the related supersymmetric hyperbolic sigma model, we give an alternative derivation of these two martingales. They turn out to be the first two instances in an infinite hierarchy of martingales, derived from a generating function.","authors_text":"Franz Merkl, Margherita Disertori, Silke W.W. Rolles","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-23T09:50:14Z","title":"A supersymmetric approach to martingales related to the vertex-reinforced jump process"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07157","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:a56fe17775c24994be3e8d9692ef44fd9f87bf4a1c4124abc251a90da1106dc7","target":"record","created_at":"2026-05-18T01:26:12Z","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":"ac52f5119fd8872f8e65e1a86240adad58b3a67836ff3b268f7fc063d6821e34","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-23T09:50:14Z","title_canon_sha256":"cf535195dc44631b3cfb40312cf8e7d95a0492573f557560cc8f8daa0c6c841e"},"schema_version":"1.0","source":{"id":"1511.07157","kind":"arxiv","version":1}},"canonical_sha256":"c03529c166bc4e51ffef4f40730374ff1543d0e23713267ab509c81a8fe97d7d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c03529c166bc4e51ffef4f40730374ff1543d0e23713267ab509c81a8fe97d7d","first_computed_at":"2026-05-18T01:26:12.080217Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:12.080217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7fidU5eMsWBIAQP0RsRPzsV43/Jfjq4sM1OBu1yElGLLA1dM02gA2EzAvfy1x3+sjGosMK3y7XKNgWPQUXKRBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:12.080714Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.07157","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a56fe17775c24994be3e8d9692ef44fd9f87bf4a1c4124abc251a90da1106dc7","sha256:1461e0afba8e5e6b847605fcdf809997faf24c2a64bc40f3b83ead57489b55db"],"state_sha256":"df6f79710a5eb8bcb8b007105dc8c91c219eb2e3e17c18da531731897788521b"}