{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:H3PH2FFIVMJCPIS6ARXGBMIMZR","short_pith_number":"pith:H3PH2FFI","canonical_record":{"source":{"id":"1611.06640","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-21T03:30:28Z","cross_cats_sorted":["math-ph","math.MP","math.RT"],"title_canon_sha256":"786d1b175424c4a8e5bcda025ce3e4828076e35ea86a86a1fe2f31e27bf904e3","abstract_canon_sha256":"96ed66852ededec4b4ffe4f61b6813bda89f11cae2df1183546de89bb56c3802"},"schema_version":"1.0"},"canonical_sha256":"3ede7d14a8ab1227a25e046e60b10ccc51700ce1720ecf8b69b8c1a123cbbe93","source":{"kind":"arxiv","id":"1611.06640","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.06640","created_at":"2026-05-18T00:57:33Z"},{"alias_kind":"arxiv_version","alias_value":"1611.06640v1","created_at":"2026-05-18T00:57:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.06640","created_at":"2026-05-18T00:57:33Z"},{"alias_kind":"pith_short_12","alias_value":"H3PH2FFIVMJC","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"H3PH2FFIVMJCPIS6","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"H3PH2FFI","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:H3PH2FFIVMJCPIS6ARXGBMIMZR","target":"record","payload":{"canonical_record":{"source":{"id":"1611.06640","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-21T03:30:28Z","cross_cats_sorted":["math-ph","math.MP","math.RT"],"title_canon_sha256":"786d1b175424c4a8e5bcda025ce3e4828076e35ea86a86a1fe2f31e27bf904e3","abstract_canon_sha256":"96ed66852ededec4b4ffe4f61b6813bda89f11cae2df1183546de89bb56c3802"},"schema_version":"1.0"},"canonical_sha256":"3ede7d14a8ab1227a25e046e60b10ccc51700ce1720ecf8b69b8c1a123cbbe93","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:33.299953Z","signature_b64":"9meXHGSamZF7D5r9JJ3h5OcXE0jGacj2D0fupeJrao6pP5ZTg+h7MuvhhokEteTzLHXQS7yNgs/q0HhTilwcAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ede7d14a8ab1227a25e046e60b10ccc51700ce1720ecf8b69b8c1a123cbbe93","last_reissued_at":"2026-05-18T00:57:33.299532Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:33.299532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.06640","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":"2026-05-18T00:57:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ICYo5w+rkQJdWuynx2mrLTRzuMAvtE/q+DEYats/yh0dVCHJSExkM77af2Ns+QzBaumoOLormuSfumUg0Ua1CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:28:54.290304Z"},"content_sha256":"0d468b4b8fa714ee9004ca1d44d7c0504d0ac506d38c8043bfb8b86d8ac3b290","schema_version":"1.0","event_id":"sha256:0d468b4b8fa714ee9004ca1d44d7c0504d0ac506d38c8043bfb8b86d8ac3b290"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:H3PH2FFIVMJCPIS6ARXGBMIMZR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Combinatorics and Representation Theory for Generalized Permutohedra I: Simplicial Plates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.RT"],"primary_cat":"math.CO","authors_text":"Nick Early","submitted_at":"2016-11-21T03:30:28Z","abstract_excerpt":"In this paper, we announce results from our thesis, which studies for the first time the categorification of the theory of generalized permutohedra. The vector spaces in the categorification are tightly constrained by certain continuity relations which appeared in physics in the mid 20th century. We describe here the action of the symmetric group on the vector spaces in this categorification. Generalized permutohedra are replaced by vector spaces of characteristic functions of polyhedral cones about faces of permutohedra, called plates, due to A. Ocneanu. The symmetric group acts on plates by "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06640","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":"2026-05-18T00:57:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4EBHzVt+rIV75VMabec7WT1eak14DxJ1/3Z3Lzk7Obxfv7/xB++W8npNfYIMJR+jsDX/UWXdgmUi7KTIeGK9Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:28:54.291036Z"},"content_sha256":"c4c059a38a5d04b462426e7d5c8fbd2a5398c53b84a90128fa8cae90f7b3b19e","schema_version":"1.0","event_id":"sha256:c4c059a38a5d04b462426e7d5c8fbd2a5398c53b84a90128fa8cae90f7b3b19e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H3PH2FFIVMJCPIS6ARXGBMIMZR/bundle.json","state_url":"https://pith.science/pith/H3PH2FFIVMJCPIS6ARXGBMIMZR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H3PH2FFIVMJCPIS6ARXGBMIMZR/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":"2026-06-07T16:28:54Z","links":{"resolver":"https://pith.science/pith/H3PH2FFIVMJCPIS6ARXGBMIMZR","bundle":"https://pith.science/pith/H3PH2FFIVMJCPIS6ARXGBMIMZR/bundle.json","state":"https://pith.science/pith/H3PH2FFIVMJCPIS6ARXGBMIMZR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H3PH2FFIVMJCPIS6ARXGBMIMZR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:H3PH2FFIVMJCPIS6ARXGBMIMZR","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":"96ed66852ededec4b4ffe4f61b6813bda89f11cae2df1183546de89bb56c3802","cross_cats_sorted":["math-ph","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-21T03:30:28Z","title_canon_sha256":"786d1b175424c4a8e5bcda025ce3e4828076e35ea86a86a1fe2f31e27bf904e3"},"schema_version":"1.0","source":{"id":"1611.06640","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.06640","created_at":"2026-05-18T00:57:33Z"},{"alias_kind":"arxiv_version","alias_value":"1611.06640v1","created_at":"2026-05-18T00:57:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.06640","created_at":"2026-05-18T00:57:33Z"},{"alias_kind":"pith_short_12","alias_value":"H3PH2FFIVMJC","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"H3PH2FFIVMJCPIS6","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"H3PH2FFI","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:c4c059a38a5d04b462426e7d5c8fbd2a5398c53b84a90128fa8cae90f7b3b19e","target":"graph","created_at":"2026-05-18T00:57:33Z","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":"In this paper, we announce results from our thesis, which studies for the first time the categorification of the theory of generalized permutohedra. The vector spaces in the categorification are tightly constrained by certain continuity relations which appeared in physics in the mid 20th century. We describe here the action of the symmetric group on the vector spaces in this categorification. Generalized permutohedra are replaced by vector spaces of characteristic functions of polyhedral cones about faces of permutohedra, called plates, due to A. Ocneanu. The symmetric group acts on plates by ","authors_text":"Nick Early","cross_cats":["math-ph","math.MP","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-21T03:30:28Z","title":"Combinatorics and Representation Theory for Generalized Permutohedra I: Simplicial Plates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06640","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":"sha256:0d468b4b8fa714ee9004ca1d44d7c0504d0ac506d38c8043bfb8b86d8ac3b290","target":"record","created_at":"2026-05-18T00:57:33Z","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":"96ed66852ededec4b4ffe4f61b6813bda89f11cae2df1183546de89bb56c3802","cross_cats_sorted":["math-ph","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-21T03:30:28Z","title_canon_sha256":"786d1b175424c4a8e5bcda025ce3e4828076e35ea86a86a1fe2f31e27bf904e3"},"schema_version":"1.0","source":{"id":"1611.06640","kind":"arxiv","version":1}},"canonical_sha256":"3ede7d14a8ab1227a25e046e60b10ccc51700ce1720ecf8b69b8c1a123cbbe93","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ede7d14a8ab1227a25e046e60b10ccc51700ce1720ecf8b69b8c1a123cbbe93","first_computed_at":"2026-05-18T00:57:33.299532Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:33.299532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9meXHGSamZF7D5r9JJ3h5OcXE0jGacj2D0fupeJrao6pP5ZTg+h7MuvhhokEteTzLHXQS7yNgs/q0HhTilwcAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:33.299953Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.06640","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d468b4b8fa714ee9004ca1d44d7c0504d0ac506d38c8043bfb8b86d8ac3b290","sha256:c4c059a38a5d04b462426e7d5c8fbd2a5398c53b84a90128fa8cae90f7b3b19e"],"state_sha256":"e7db88bfc8a432cb29b9560fede7b891ffe10609eeb955b9f12f3abd0dd9be62"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4IgyBPhfUeF2hBRi4xVgJgtp3kj/asr9ihLzSZHU9DI0PKffF/B/tdqUW29XeBPq9gWas61RHPEO//l43K/TDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T16:28:54.295438Z","bundle_sha256":"549b1603f9780447be4397f4d5ce70f3f4f5b6669bd16d3151d7919274a42500"}}