{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:7KYDCF7EIYCSO5DSK2X3J7VR4X","short_pith_number":"pith:7KYDCF7E","canonical_record":{"source":{"id":"1802.08977","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-02-25T09:49:40Z","cross_cats_sorted":["math-ph","math.MP","math.RT"],"title_canon_sha256":"1f937280d5ed7fa38d1cd46b2b88e394ef8902a16ec8becb1f2c456030f35738","abstract_canon_sha256":"4626298d477719aa80e8119719e4055d98c116c3ff2aca5d5280fb8c998a051f"},"schema_version":"1.0"},"canonical_sha256":"fab03117e4460527747256afb4feb1e5d463d73c03983e1e5a3616996d0bfdeb","source":{"kind":"arxiv","id":"1802.08977","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.08977","created_at":"2026-05-17T23:41:56Z"},{"alias_kind":"arxiv_version","alias_value":"1802.08977v1","created_at":"2026-05-17T23:41:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.08977","created_at":"2026-05-17T23:41:56Z"},{"alias_kind":"pith_short_12","alias_value":"7KYDCF7EIYCS","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7KYDCF7EIYCSO5DS","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7KYDCF7E","created_at":"2026-05-18T12:32:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:7KYDCF7EIYCSO5DSK2X3J7VR4X","target":"record","payload":{"canonical_record":{"source":{"id":"1802.08977","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-02-25T09:49:40Z","cross_cats_sorted":["math-ph","math.MP","math.RT"],"title_canon_sha256":"1f937280d5ed7fa38d1cd46b2b88e394ef8902a16ec8becb1f2c456030f35738","abstract_canon_sha256":"4626298d477719aa80e8119719e4055d98c116c3ff2aca5d5280fb8c998a051f"},"schema_version":"1.0"},"canonical_sha256":"fab03117e4460527747256afb4feb1e5d463d73c03983e1e5a3616996d0bfdeb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:56.393849Z","signature_b64":"t9YeMX1mDQUmWoV9qeteG4VXKDOeX/U+O4Du8j0nsHqgDy/pPp1LXbnuve0zWkvbSEcr8w7Q/XvP9TzYsfNrCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fab03117e4460527747256afb4feb1e5d463d73c03983e1e5a3616996d0bfdeb","last_reissued_at":"2026-05-17T23:41:56.393131Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:56.393131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.08977","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":"2026-05-17T23:41:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F016QbGANJFu9MGAxi36S++W7oGkIkOk3xD8rqXK8Iq5SjUIVOkxsIjUDKX7xuQm6aTJShowFcFTploYBZIqCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T21:52:22.099053Z"},"content_sha256":"2f7942b96dd45d26aa6822bcdc63042418b31acb566fd906bdd7db00c39cf0e5","schema_version":"1.0","event_id":"sha256:2f7942b96dd45d26aa6822bcdc63042418b31acb566fd906bdd7db00c39cf0e5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:7KYDCF7EIYCSO5DSK2X3J7VR4X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cylindric Reverse Plane Partitions and 2D TQFT","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.RT"],"primary_cat":"math.CO","authors_text":"Christian Korff, David Palazzo","submitted_at":"2018-02-25T09:49:40Z","abstract_excerpt":"The ring of symmetric functions carries the structure of a Hopf algebra. When computing the coproduct of complete symmetric functions $h_\\lambda$ one arrives at weighted sums over reverse plane partitions (RPP) involving binomial coefficients. Employing the action of the extended affine symmetric group at fixed level $n$ we generalise these weighted sums to cylindric RPP and define cylindric complete symmetric functions. The latter are shown to be $h$-positive, that is, their expansions coefficients in the basis of complete symmetric functions are non-negative integers. We state an explicit fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.08977","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":""},"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":"2026-05-17T23:41:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Spr/AQqHj8MsmxOweAsKR8e+zNCccXo3PESyAm2QTNgpQKQUPPlx4PQTZJaU/7JopLtJzrhFDX71QAz3MqcbCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T21:52:22.099409Z"},"content_sha256":"9a31dc993bfcc4e2bd0a1cd6777c4320bf78ce0d2c937d4a31095b5ae8a4f171","schema_version":"1.0","event_id":"sha256:9a31dc993bfcc4e2bd0a1cd6777c4320bf78ce0d2c937d4a31095b5ae8a4f171"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7KYDCF7EIYCSO5DSK2X3J7VR4X/bundle.json","state_url":"https://pith.science/pith/7KYDCF7EIYCSO5DSK2X3J7VR4X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7KYDCF7EIYCSO5DSK2X3J7VR4X/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":"2026-06-28T21:52:22Z","links":{"resolver":"https://pith.science/pith/7KYDCF7EIYCSO5DSK2X3J7VR4X","bundle":"https://pith.science/pith/7KYDCF7EIYCSO5DSK2X3J7VR4X/bundle.json","state":"https://pith.science/pith/7KYDCF7EIYCSO5DSK2X3J7VR4X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7KYDCF7EIYCSO5DSK2X3J7VR4X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:7KYDCF7EIYCSO5DSK2X3J7VR4X","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":"4626298d477719aa80e8119719e4055d98c116c3ff2aca5d5280fb8c998a051f","cross_cats_sorted":["math-ph","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-02-25T09:49:40Z","title_canon_sha256":"1f937280d5ed7fa38d1cd46b2b88e394ef8902a16ec8becb1f2c456030f35738"},"schema_version":"1.0","source":{"id":"1802.08977","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.08977","created_at":"2026-05-17T23:41:56Z"},{"alias_kind":"arxiv_version","alias_value":"1802.08977v1","created_at":"2026-05-17T23:41:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.08977","created_at":"2026-05-17T23:41:56Z"},{"alias_kind":"pith_short_12","alias_value":"7KYDCF7EIYCS","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7KYDCF7EIYCSO5DS","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7KYDCF7E","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:9a31dc993bfcc4e2bd0a1cd6777c4320bf78ce0d2c937d4a31095b5ae8a4f171","target":"graph","created_at":"2026-05-17T23:41:56Z","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":"The ring of symmetric functions carries the structure of a Hopf algebra. When computing the coproduct of complete symmetric functions $h_\\lambda$ one arrives at weighted sums over reverse plane partitions (RPP) involving binomial coefficients. Employing the action of the extended affine symmetric group at fixed level $n$ we generalise these weighted sums to cylindric RPP and define cylindric complete symmetric functions. The latter are shown to be $h$-positive, that is, their expansions coefficients in the basis of complete symmetric functions are non-negative integers. We state an explicit fo","authors_text":"Christian Korff, David Palazzo","cross_cats":["math-ph","math.MP","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-02-25T09:49:40Z","title":"Cylindric Reverse Plane Partitions and 2D TQFT"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.08977","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":"sha256:2f7942b96dd45d26aa6822bcdc63042418b31acb566fd906bdd7db00c39cf0e5","target":"record","created_at":"2026-05-17T23:41:56Z","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":"4626298d477719aa80e8119719e4055d98c116c3ff2aca5d5280fb8c998a051f","cross_cats_sorted":["math-ph","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-02-25T09:49:40Z","title_canon_sha256":"1f937280d5ed7fa38d1cd46b2b88e394ef8902a16ec8becb1f2c456030f35738"},"schema_version":"1.0","source":{"id":"1802.08977","kind":"arxiv","version":1}},"canonical_sha256":"fab03117e4460527747256afb4feb1e5d463d73c03983e1e5a3616996d0bfdeb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fab03117e4460527747256afb4feb1e5d463d73c03983e1e5a3616996d0bfdeb","first_computed_at":"2026-05-17T23:41:56.393131Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:56.393131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t9YeMX1mDQUmWoV9qeteG4VXKDOeX/U+O4Du8j0nsHqgDy/pPp1LXbnuve0zWkvbSEcr8w7Q/XvP9TzYsfNrCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:56.393849Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.08977","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f7942b96dd45d26aa6822bcdc63042418b31acb566fd906bdd7db00c39cf0e5","sha256:9a31dc993bfcc4e2bd0a1cd6777c4320bf78ce0d2c937d4a31095b5ae8a4f171"],"state_sha256":"7fd332dfa0537935dc66cdbeae012279208481d337e6d797ef0c4b4f50359689"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7lHAetyJ/RO4vpQrII3s9qJmnm0Z/KFTuWt2DHCWSfTtPlR/4sXlSNUo+aGlNtOILJ4XXnFxEaryGfc+6n4dBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T21:52:22.102624Z","bundle_sha256":"f03980d5a4da7d50da352aa1f6023efa7e8c47cc0e89387a27bb5c7c9c6dfd77"}}