{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:AJAR7RQNV6TBSTLYNB37BLK4RC","short_pith_number":"pith:AJAR7RQN","canonical_record":{"source":{"id":"2302.03092","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2023-02-06T19:48:49Z","cross_cats_sorted":["hep-th","math.AG","math.MP","math.NT","math.RT"],"title_canon_sha256":"60de7ae26c88feec82da7194c4fdfa8342ac80d2d4142dc2311516f5d916814c","abstract_canon_sha256":"03e93431de0a2a0d4aa4f0002f911009189465edbc3bce72659502270ebdd195"},"schema_version":"1.0"},"canonical_sha256":"02411fc60dafa6194d786877f0ad5c88ade64e16a2418a01866bcb55ca307d18","source":{"kind":"arxiv","id":"2302.03092","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.03092","created_at":"2026-07-05T06:12:44Z"},{"alias_kind":"arxiv_version","alias_value":"2302.03092v3","created_at":"2026-07-05T06:12:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.03092","created_at":"2026-07-05T06:12:44Z"},{"alias_kind":"pith_short_12","alias_value":"AJAR7RQNV6TB","created_at":"2026-07-05T06:12:44Z"},{"alias_kind":"pith_short_16","alias_value":"AJAR7RQNV6TBSTLY","created_at":"2026-07-05T06:12:44Z"},{"alias_kind":"pith_short_8","alias_value":"AJAR7RQN","created_at":"2026-07-05T06:12:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:AJAR7RQNV6TBSTLYNB37BLK4RC","target":"record","payload":{"canonical_record":{"source":{"id":"2302.03092","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2023-02-06T19:48:49Z","cross_cats_sorted":["hep-th","math.AG","math.MP","math.NT","math.RT"],"title_canon_sha256":"60de7ae26c88feec82da7194c4fdfa8342ac80d2d4142dc2311516f5d916814c","abstract_canon_sha256":"03e93431de0a2a0d4aa4f0002f911009189465edbc3bce72659502270ebdd195"},"schema_version":"1.0"},"canonical_sha256":"02411fc60dafa6194d786877f0ad5c88ade64e16a2418a01866bcb55ca307d18","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:12:44.010745Z","signature_b64":"uJY/9v9NnwAbqyM5Urr+lge+CD+44+DApuM/J8IW847vwjIga/7JmS30Et/oV42wq6Z6EEzVd/lNdAZpJjV4DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"02411fc60dafa6194d786877f0ad5c88ade64e16a2418a01866bcb55ca307d18","last_reissued_at":"2026-07-05T06:12:44.010292Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:12:44.010292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2302.03092","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:12:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RICDUx0C+MFb8GAPWxLO+HYIzYnBJZM6CgvGLb5v24y0tJQHaLeLIcLAi7gelBO9G6jgRYXzCA8U8EInGs9SAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T14:38:29.562335Z"},"content_sha256":"da56e247ef2a6e3c6237132386554e47afa16fe0ad574de495dc5c26e14288c8","schema_version":"1.0","event_id":"sha256:da56e247ef2a6e3c6237132386554e47afa16fe0ad574de495dc5c26e14288c8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:AJAR7RQNV6TBSTLYNB37BLK4RC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The p-adic approximations of vertex functions via 3D-mirror symmetry","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th","math.AG","math.MP","math.NT","math.RT"],"primary_cat":"math-ph","authors_text":"Alexander Varchenko, Andrey Smirnov","submitted_at":"2023-02-06T19:48:49Z","abstract_excerpt":"Using the $3D$ mirror symmetry we construct a system of polynomials $T_s(z)$ with integral coefficients which solve the quantum differential equitation of $X=T^{*} Gr(k,n)$ modulo $p^s$, where $p$ is a prime number. We show that the sequence $T_s(z)$ converges in the $p$-adic norm to the Okounkov's vertex function of $X$ as $s\\to \\infty$. We prove that $T_s(z)$ satisfy Dwork-type congruences which lead to a new infinite product presentation of the vertex function modulo $p^s$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.03092","kind":"arxiv","version":3},"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/2302.03092/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":"2026-07-05T06:12:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yr8IC1HlggFauQ5NyrYFNP70k04nKTBFwVbAKU2DRkfo5H/V0gz8aZiEnaekXQe6B2pw7KXSxP0bU0/8ZAg2BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T14:38:29.562891Z"},"content_sha256":"182f311cc1cd2ddd933440a6f88d6a183d7d2c3d89743042137973e71add9dbc","schema_version":"1.0","event_id":"sha256:182f311cc1cd2ddd933440a6f88d6a183d7d2c3d89743042137973e71add9dbc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AJAR7RQNV6TBSTLYNB37BLK4RC/bundle.json","state_url":"https://pith.science/pith/AJAR7RQNV6TBSTLYNB37BLK4RC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AJAR7RQNV6TBSTLYNB37BLK4RC/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":"2026-08-23T14:38:29Z","links":{"resolver":"https://pith.science/pith/AJAR7RQNV6TBSTLYNB37BLK4RC","bundle":"https://pith.science/pith/AJAR7RQNV6TBSTLYNB37BLK4RC/bundle.json","state":"https://pith.science/pith/AJAR7RQNV6TBSTLYNB37BLK4RC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AJAR7RQNV6TBSTLYNB37BLK4RC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:AJAR7RQNV6TBSTLYNB37BLK4RC","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":"03e93431de0a2a0d4aa4f0002f911009189465edbc3bce72659502270ebdd195","cross_cats_sorted":["hep-th","math.AG","math.MP","math.NT","math.RT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2023-02-06T19:48:49Z","title_canon_sha256":"60de7ae26c88feec82da7194c4fdfa8342ac80d2d4142dc2311516f5d916814c"},"schema_version":"1.0","source":{"id":"2302.03092","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.03092","created_at":"2026-07-05T06:12:44Z"},{"alias_kind":"arxiv_version","alias_value":"2302.03092v3","created_at":"2026-07-05T06:12:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.03092","created_at":"2026-07-05T06:12:44Z"},{"alias_kind":"pith_short_12","alias_value":"AJAR7RQNV6TB","created_at":"2026-07-05T06:12:44Z"},{"alias_kind":"pith_short_16","alias_value":"AJAR7RQNV6TBSTLY","created_at":"2026-07-05T06:12:44Z"},{"alias_kind":"pith_short_8","alias_value":"AJAR7RQN","created_at":"2026-07-05T06:12:44Z"}],"graph_snapshots":[{"event_id":"sha256:182f311cc1cd2ddd933440a6f88d6a183d7d2c3d89743042137973e71add9dbc","target":"graph","created_at":"2026-07-05T06:12:44Z","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/2302.03092/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Using the $3D$ mirror symmetry we construct a system of polynomials $T_s(z)$ with integral coefficients which solve the quantum differential equitation of $X=T^{*} Gr(k,n)$ modulo $p^s$, where $p$ is a prime number. We show that the sequence $T_s(z)$ converges in the $p$-adic norm to the Okounkov's vertex function of $X$ as $s\\to \\infty$. We prove that $T_s(z)$ satisfy Dwork-type congruences which lead to a new infinite product presentation of the vertex function modulo $p^s$.","authors_text":"Alexander Varchenko, Andrey Smirnov","cross_cats":["hep-th","math.AG","math.MP","math.NT","math.RT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2023-02-06T19:48:49Z","title":"The p-adic approximations of vertex functions via 3D-mirror symmetry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.03092","kind":"arxiv","version":3},"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:da56e247ef2a6e3c6237132386554e47afa16fe0ad574de495dc5c26e14288c8","target":"record","created_at":"2026-07-05T06:12:44Z","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":"03e93431de0a2a0d4aa4f0002f911009189465edbc3bce72659502270ebdd195","cross_cats_sorted":["hep-th","math.AG","math.MP","math.NT","math.RT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2023-02-06T19:48:49Z","title_canon_sha256":"60de7ae26c88feec82da7194c4fdfa8342ac80d2d4142dc2311516f5d916814c"},"schema_version":"1.0","source":{"id":"2302.03092","kind":"arxiv","version":3}},"canonical_sha256":"02411fc60dafa6194d786877f0ad5c88ade64e16a2418a01866bcb55ca307d18","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"02411fc60dafa6194d786877f0ad5c88ade64e16a2418a01866bcb55ca307d18","first_computed_at":"2026-07-05T06:12:44.010292Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:12:44.010292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uJY/9v9NnwAbqyM5Urr+lge+CD+44+DApuM/J8IW847vwjIga/7JmS30Et/oV42wq6Z6EEzVd/lNdAZpJjV4DA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:12:44.010745Z","signed_message":"canonical_sha256_bytes"},"source_id":"2302.03092","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:da56e247ef2a6e3c6237132386554e47afa16fe0ad574de495dc5c26e14288c8","sha256:182f311cc1cd2ddd933440a6f88d6a183d7d2c3d89743042137973e71add9dbc"],"state_sha256":"960c935afcfb5fa87e8e24316a54d9d91422505ba5fcccba022f7486c318e8ad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cRtCszhZNG3kkOH5Iq6br0TIPSfmS+sFaprlrUiQo7pMjAjzO85L1LaCIXDX4k/uuQIyzlhv/gNjWzUzm0BBCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-23T14:38:29.569827Z","bundle_sha256":"004537dbc505b262762e7eaf27495e93ebab4f888981e5d2d584f54e8e1451d1"}}