{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:UFRUPI72HKYIWJWGOWKDMMT6WX","short_pith_number":"pith:UFRUPI72","canonical_record":{"source":{"id":"1307.3379","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-07-12T08:57:20Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"2ae0c26681fc886e9a05549d980e2a5bb4acba6706635ec7233a9b33da64f713","abstract_canon_sha256":"892c4ebcd6ae0f9fe852ef066792a016fddee36bc6a88f5f700aac56afec2af0"},"schema_version":"1.0"},"canonical_sha256":"a16347a3fa3ab08b26c6759436327eb5c5c5fc9150e92db9b88d667f3901f45e","source":{"kind":"arxiv","id":"1307.3379","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.3379","created_at":"2026-05-18T01:29:11Z"},{"alias_kind":"arxiv_version","alias_value":"1307.3379v2","created_at":"2026-05-18T01:29:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.3379","created_at":"2026-05-18T01:29:11Z"},{"alias_kind":"pith_short_12","alias_value":"UFRUPI72HKYI","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"UFRUPI72HKYIWJWG","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"UFRUPI72","created_at":"2026-05-18T12:28:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:UFRUPI72HKYIWJWGOWKDMMT6WX","target":"record","payload":{"canonical_record":{"source":{"id":"1307.3379","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-07-12T08:57:20Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"2ae0c26681fc886e9a05549d980e2a5bb4acba6706635ec7233a9b33da64f713","abstract_canon_sha256":"892c4ebcd6ae0f9fe852ef066792a016fddee36bc6a88f5f700aac56afec2af0"},"schema_version":"1.0"},"canonical_sha256":"a16347a3fa3ab08b26c6759436327eb5c5c5fc9150e92db9b88d667f3901f45e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:11.797269Z","signature_b64":"+CpDeVgCPIsC3CCY3n9Yjr/9+WXt4fNQjz+JWi72aN4k8Spe/L6uHCZyZQ9PIfXdfEdSteAWSK0+tRpydJ6WCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a16347a3fa3ab08b26c6759436327eb5c5c5fc9150e92db9b88d667f3901f45e","last_reissued_at":"2026-05-18T01:29:11.796713Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:11.796713Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.3379","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":"2026-05-18T01:29:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+WvttnwEzQCc05i4FSexd5H7MofhPrBmhVp8sxak0uPWKY1qGUN4Z7vQKRljpKhWUctj4Jm6lKDDaI/lBNcFCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T03:32:27.417931Z"},"content_sha256":"f0c139608a37adacd1891c9ae4804271cd95ecb3ad6e558666410eec332cc92d","schema_version":"1.0","event_id":"sha256:f0c139608a37adacd1891c9ae4804271cd95ecb3ad6e558666410eec332cc92d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:UFRUPI72HKYIWJWGOWKDMMT6WX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Purity for graded potentials and quantum cluster positivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Balazs Szendroi, Ben Davison, Davesh Maulik, Joerg Schuermann","submitted_at":"2013-07-12T08:57:20Z","abstract_excerpt":"Consider a smooth quasiprojective variety X equipped with a C*-action, and a regular function f: X -> C which is C*-equivariant with respect to a positive weight action on the base. We prove the purity of the mixed Hodge structure and the hard Lefschetz theorem on the cohomology of the vanishing cycle complex of f on proper components of the critical locus of f, generalizing a result of Steenbrink for isolated quasi-homogeneous singularities. Building on work of Kontsevich-Soibelman, Nagao and Efimov, we use this result to prove the quantum positivity conjecture for cluster mutations for all q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3379","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":""},"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":"2026-05-18T01:29:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vdVtwrZmh5FqRXf3BL2EOMnDqBLTFtkSsh7WvTQDNjnzApHloUsjwD6CQE7/qW1la6kl/SKy8MsS2/6lTRDoAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T03:32:27.418270Z"},"content_sha256":"c7bb03157be1efdc55a74c49c49aeded7729f40e0fda0a1cddb4e184b7e73ba4","schema_version":"1.0","event_id":"sha256:c7bb03157be1efdc55a74c49c49aeded7729f40e0fda0a1cddb4e184b7e73ba4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UFRUPI72HKYIWJWGOWKDMMT6WX/bundle.json","state_url":"https://pith.science/pith/UFRUPI72HKYIWJWGOWKDMMT6WX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UFRUPI72HKYIWJWGOWKDMMT6WX/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":"2026-06-22T03:32:27Z","links":{"resolver":"https://pith.science/pith/UFRUPI72HKYIWJWGOWKDMMT6WX","bundle":"https://pith.science/pith/UFRUPI72HKYIWJWGOWKDMMT6WX/bundle.json","state":"https://pith.science/pith/UFRUPI72HKYIWJWGOWKDMMT6WX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UFRUPI72HKYIWJWGOWKDMMT6WX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:UFRUPI72HKYIWJWGOWKDMMT6WX","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":"892c4ebcd6ae0f9fe852ef066792a016fddee36bc6a88f5f700aac56afec2af0","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-07-12T08:57:20Z","title_canon_sha256":"2ae0c26681fc886e9a05549d980e2a5bb4acba6706635ec7233a9b33da64f713"},"schema_version":"1.0","source":{"id":"1307.3379","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.3379","created_at":"2026-05-18T01:29:11Z"},{"alias_kind":"arxiv_version","alias_value":"1307.3379v2","created_at":"2026-05-18T01:29:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.3379","created_at":"2026-05-18T01:29:11Z"},{"alias_kind":"pith_short_12","alias_value":"UFRUPI72HKYI","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"UFRUPI72HKYIWJWG","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"UFRUPI72","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:c7bb03157be1efdc55a74c49c49aeded7729f40e0fda0a1cddb4e184b7e73ba4","target":"graph","created_at":"2026-05-18T01:29:11Z","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":"Consider a smooth quasiprojective variety X equipped with a C*-action, and a regular function f: X -> C which is C*-equivariant with respect to a positive weight action on the base. We prove the purity of the mixed Hodge structure and the hard Lefschetz theorem on the cohomology of the vanishing cycle complex of f on proper components of the critical locus of f, generalizing a result of Steenbrink for isolated quasi-homogeneous singularities. Building on work of Kontsevich-Soibelman, Nagao and Efimov, we use this result to prove the quantum positivity conjecture for cluster mutations for all q","authors_text":"Balazs Szendroi, Ben Davison, Davesh Maulik, Joerg Schuermann","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-07-12T08:57:20Z","title":"Purity for graded potentials and quantum cluster positivity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3379","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:f0c139608a37adacd1891c9ae4804271cd95ecb3ad6e558666410eec332cc92d","target":"record","created_at":"2026-05-18T01:29:11Z","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":"892c4ebcd6ae0f9fe852ef066792a016fddee36bc6a88f5f700aac56afec2af0","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-07-12T08:57:20Z","title_canon_sha256":"2ae0c26681fc886e9a05549d980e2a5bb4acba6706635ec7233a9b33da64f713"},"schema_version":"1.0","source":{"id":"1307.3379","kind":"arxiv","version":2}},"canonical_sha256":"a16347a3fa3ab08b26c6759436327eb5c5c5fc9150e92db9b88d667f3901f45e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a16347a3fa3ab08b26c6759436327eb5c5c5fc9150e92db9b88d667f3901f45e","first_computed_at":"2026-05-18T01:29:11.796713Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:11.796713Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+CpDeVgCPIsC3CCY3n9Yjr/9+WXt4fNQjz+JWi72aN4k8Spe/L6uHCZyZQ9PIfXdfEdSteAWSK0+tRpydJ6WCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:11.797269Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.3379","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f0c139608a37adacd1891c9ae4804271cd95ecb3ad6e558666410eec332cc92d","sha256:c7bb03157be1efdc55a74c49c49aeded7729f40e0fda0a1cddb4e184b7e73ba4"],"state_sha256":"ecc956ad07fd12a1b93e735daf77f473288436653e9a418fba67806b7036a009"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B65moN17Tcj7wjeFsdZ8BuGjHZef91DSS+MFCHEzQaJirbNJl0GpjLit+2/a0V7BxxbDqBDOqTl546sYXVGXBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T03:32:27.420118Z","bundle_sha256":"d18ae91be17446471a51c29ad790c7bf1ffca452a818630387722b5f2ad3fbe1"}}