{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:TZICRGN6AC7M52FMJW7RE7M2KH","short_pith_number":"pith:TZICRGN6","canonical_record":{"source":{"id":"1905.07692","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-19T06:52:39Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"d061077b81bf4dec852c1dbffa21d811ca21f8c0f59b02761cf1e5dcb8e0d11a","abstract_canon_sha256":"6c9e989c5f00374d70b8f16f528f03a98b1b70182ecc1ccdc7272168236152a7"},"schema_version":"1.0"},"canonical_sha256":"9e502899be00becee8ac4dbf127d9a51c022415743b4a14ce60fa6d48eaaa925","source":{"kind":"arxiv","id":"1905.07692","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.07692","created_at":"2026-07-05T01:43:37Z"},{"alias_kind":"arxiv_version","alias_value":"1905.07692v4","created_at":"2026-07-05T01:43:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.07692","created_at":"2026-07-05T01:43:37Z"},{"alias_kind":"pith_short_12","alias_value":"TZICRGN6AC7M","created_at":"2026-07-05T01:43:37Z"},{"alias_kind":"pith_short_16","alias_value":"TZICRGN6AC7M52FM","created_at":"2026-07-05T01:43:37Z"},{"alias_kind":"pith_short_8","alias_value":"TZICRGN6","created_at":"2026-07-05T01:43:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:TZICRGN6AC7M52FMJW7RE7M2KH","target":"record","payload":{"canonical_record":{"source":{"id":"1905.07692","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-19T06:52:39Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"d061077b81bf4dec852c1dbffa21d811ca21f8c0f59b02761cf1e5dcb8e0d11a","abstract_canon_sha256":"6c9e989c5f00374d70b8f16f528f03a98b1b70182ecc1ccdc7272168236152a7"},"schema_version":"1.0"},"canonical_sha256":"9e502899be00becee8ac4dbf127d9a51c022415743b4a14ce60fa6d48eaaa925","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:43:37.430239Z","signature_b64":"uvayPiZbouWgP1j/DyGfD+puOWjFZ2VPupVuELCHUuoYHcj4YCQut84ixMVpfuLbX5lAKQLPY7yReo8WRCEyAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e502899be00becee8ac4dbf127d9a51c022415743b4a14ce60fa6d48eaaa925","last_reissued_at":"2026-07-05T01:43:37.429481Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:43:37.429481Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.07692","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:43:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gZJSMxZwAvLDP7JEuJ9NFBrrE+Cifs45H0g4KEJm9NGLA//IGmVSgQujU1bEYp44qfj2nIRlk7KNCqfgwsDBDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T20:34:26.619795Z"},"content_sha256":"d44eabe77a7b18af8a45fffb95484f42fba92e5deae2a2f0a7d291e8a38af142","schema_version":"1.0","event_id":"sha256:d44eabe77a7b18af8a45fffb95484f42fba92e5deae2a2f0a7d291e8a38af142"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:TZICRGN6AC7M52FMJW7RE7M2KH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Grothendieck polynomials and the Boson-Fermion correspondence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.CO","authors_text":"Shinsuke Iwao","submitted_at":"2019-05-19T06:52:39Z","abstract_excerpt":"In this paper we study algebraic and combinatorial properties of Grothendieck polynomials and their dual polynomials by means of the Boson-Fermion correspondence. We show that these symmetric functions can be expressed as a vacuum expectation value of some operator that is written in terms of free-fermions. By using the free-fermionic expressions, we obtain alternative proofs of determinantal formulas and Pieri type formulas."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.07692","kind":"arxiv","version":4},"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/1905.07692/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":"2026-07-05T01:43:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qHI6P5KFSqAU7zZ+3IYKFEwjXQPG64VA023koOPuIcjUXlkT31MppOxZzXEJjSF954Wu2FApFFC2CQLgUiU9CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T20:34:26.620323Z"},"content_sha256":"6b9cd052c642f4889c52ce23e1c979f58a6a4f475eb4c34a6dbcbff14fec4535","schema_version":"1.0","event_id":"sha256:6b9cd052c642f4889c52ce23e1c979f58a6a4f475eb4c34a6dbcbff14fec4535"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TZICRGN6AC7M52FMJW7RE7M2KH/bundle.json","state_url":"https://pith.science/pith/TZICRGN6AC7M52FMJW7RE7M2KH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TZICRGN6AC7M52FMJW7RE7M2KH/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":"2026-08-16T20:34:26Z","links":{"resolver":"https://pith.science/pith/TZICRGN6AC7M52FMJW7RE7M2KH","bundle":"https://pith.science/pith/TZICRGN6AC7M52FMJW7RE7M2KH/bundle.json","state":"https://pith.science/pith/TZICRGN6AC7M52FMJW7RE7M2KH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TZICRGN6AC7M52FMJW7RE7M2KH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:TZICRGN6AC7M52FMJW7RE7M2KH","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":"6c9e989c5f00374d70b8f16f528f03a98b1b70182ecc1ccdc7272168236152a7","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-19T06:52:39Z","title_canon_sha256":"d061077b81bf4dec852c1dbffa21d811ca21f8c0f59b02761cf1e5dcb8e0d11a"},"schema_version":"1.0","source":{"id":"1905.07692","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.07692","created_at":"2026-07-05T01:43:37Z"},{"alias_kind":"arxiv_version","alias_value":"1905.07692v4","created_at":"2026-07-05T01:43:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.07692","created_at":"2026-07-05T01:43:37Z"},{"alias_kind":"pith_short_12","alias_value":"TZICRGN6AC7M","created_at":"2026-07-05T01:43:37Z"},{"alias_kind":"pith_short_16","alias_value":"TZICRGN6AC7M52FM","created_at":"2026-07-05T01:43:37Z"},{"alias_kind":"pith_short_8","alias_value":"TZICRGN6","created_at":"2026-07-05T01:43:37Z"}],"graph_snapshots":[{"event_id":"sha256:6b9cd052c642f4889c52ce23e1c979f58a6a4f475eb4c34a6dbcbff14fec4535","target":"graph","created_at":"2026-07-05T01:43:37Z","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/1905.07692/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we study algebraic and combinatorial properties of Grothendieck polynomials and their dual polynomials by means of the Boson-Fermion correspondence. We show that these symmetric functions can be expressed as a vacuum expectation value of some operator that is written in terms of free-fermions. By using the free-fermionic expressions, we obtain alternative proofs of determinantal formulas and Pieri type formulas.","authors_text":"Shinsuke Iwao","cross_cats":["math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-19T06:52:39Z","title":"Grothendieck polynomials and the Boson-Fermion correspondence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.07692","kind":"arxiv","version":4},"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:d44eabe77a7b18af8a45fffb95484f42fba92e5deae2a2f0a7d291e8a38af142","target":"record","created_at":"2026-07-05T01:43:37Z","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":"6c9e989c5f00374d70b8f16f528f03a98b1b70182ecc1ccdc7272168236152a7","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-19T06:52:39Z","title_canon_sha256":"d061077b81bf4dec852c1dbffa21d811ca21f8c0f59b02761cf1e5dcb8e0d11a"},"schema_version":"1.0","source":{"id":"1905.07692","kind":"arxiv","version":4}},"canonical_sha256":"9e502899be00becee8ac4dbf127d9a51c022415743b4a14ce60fa6d48eaaa925","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e502899be00becee8ac4dbf127d9a51c022415743b4a14ce60fa6d48eaaa925","first_computed_at":"2026-07-05T01:43:37.429481Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:43:37.429481Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uvayPiZbouWgP1j/DyGfD+puOWjFZ2VPupVuELCHUuoYHcj4YCQut84ixMVpfuLbX5lAKQLPY7yReo8WRCEyAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:43:37.430239Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.07692","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d44eabe77a7b18af8a45fffb95484f42fba92e5deae2a2f0a7d291e8a38af142","sha256:6b9cd052c642f4889c52ce23e1c979f58a6a4f475eb4c34a6dbcbff14fec4535"],"state_sha256":"5fa183237b6a4331d62e38190d2cbde213a6520c8e5695d4d2f2630bfcc3a313"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PT595cxFsiZ7YCZoHhocJYlGiz/jpu0wW093nRojOL++uN9CcpDDxnNjT3DaP90+TeIqtbtp+Rd2+CKVmM4MDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T20:34:26.625539Z","bundle_sha256":"adcdd67dea235003a0576b95ea906932b489e5a2e53aeabedb875eba136cf388"}}