{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:JZC2I3F27QFB2ILNKD3KRA24MA","short_pith_number":"pith:JZC2I3F2","canonical_record":{"source":{"id":"0810.3322","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-10-18T15:20:07Z","cross_cats_sorted":[],"title_canon_sha256":"14f52c292b0bd90903f75de947596d43aaef67e85c27292535d866f8d62496ed","abstract_canon_sha256":"8e08b487c473697000f778b3b48e4a1be8b4333226f5730455a4b0cd054768e8"},"schema_version":"1.0"},"canonical_sha256":"4e45a46cbafc0a1d216d50f6a8835c603a66d3181011dfc92fc8ace37c990ec9","source":{"kind":"arxiv","id":"0810.3322","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.3322","created_at":"2026-05-18T03:20:19Z"},{"alias_kind":"arxiv_version","alias_value":"0810.3322v1","created_at":"2026-05-18T03:20:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.3322","created_at":"2026-05-18T03:20:19Z"},{"alias_kind":"pith_short_12","alias_value":"JZC2I3F27QFB","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"JZC2I3F27QFB2ILN","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"JZC2I3F2","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:JZC2I3F27QFB2ILNKD3KRA24MA","target":"record","payload":{"canonical_record":{"source":{"id":"0810.3322","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-10-18T15:20:07Z","cross_cats_sorted":[],"title_canon_sha256":"14f52c292b0bd90903f75de947596d43aaef67e85c27292535d866f8d62496ed","abstract_canon_sha256":"8e08b487c473697000f778b3b48e4a1be8b4333226f5730455a4b0cd054768e8"},"schema_version":"1.0"},"canonical_sha256":"4e45a46cbafc0a1d216d50f6a8835c603a66d3181011dfc92fc8ace37c990ec9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:19.238381Z","signature_b64":"+ePXSBKK/N42XU1ebuYIIgd8/8FUkOXGYnv6CAEg54jO9RMvdZVw3PxcXZnM946c9jXpXn7vWwmwckF+zHeYDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e45a46cbafc0a1d216d50f6a8835c603a66d3181011dfc92fc8ace37c990ec9","last_reissued_at":"2026-05-18T03:20:19.237637Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:19.237637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0810.3322","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":"2026-05-18T03:20:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9sOlvjd+IVyHu9aEambwnzaDmv0vu2e2bXI1eM9na6ZV10zERfzKlJSdjJstnF57orkC2uWlGShdTnuiVlm3AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T14:56:13.619574Z"},"content_sha256":"a6d7355b0e0cb614cbd077294a74f939c6d58459f4b08de724f81b420f7d9763","schema_version":"1.0","event_id":"sha256:a6d7355b0e0cb614cbd077294a74f939c6d58459f4b08de724f81b420f7d9763"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:JZC2I3F27QFB2ILNKD3KRA24MA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Clifford Algebras and Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Tanya Khovanova","submitted_at":"2008-10-18T15:20:07Z","abstract_excerpt":"I show how to associate a Clifford algebra to a graph. I describe the structure of these Clifford graph algebras and provide many examples and pictures. I describe which graphs correspond to isomorphic Clifford algebras and also discuss other related sets of graphs. This construction can be used to build models of representations of simply-laced compact Lie groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.3322","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":"2026-05-18T03:20:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u+SSDjZBXojYo3pMErcykAKQBskUh+ytn62DdIkfVj+ZZTjhAMWxaOItCQrnaUC3rkKGrT+RmJpNNjKu6pvvBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T14:56:13.619916Z"},"content_sha256":"a4a84742c33c07a2d1618b741227714dc62d48e00fe10340ef865de55ead0652","schema_version":"1.0","event_id":"sha256:a4a84742c33c07a2d1618b741227714dc62d48e00fe10340ef865de55ead0652"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JZC2I3F27QFB2ILNKD3KRA24MA/bundle.json","state_url":"https://pith.science/pith/JZC2I3F27QFB2ILNKD3KRA24MA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JZC2I3F27QFB2ILNKD3KRA24MA/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":"2026-06-29T14:56:13Z","links":{"resolver":"https://pith.science/pith/JZC2I3F27QFB2ILNKD3KRA24MA","bundle":"https://pith.science/pith/JZC2I3F27QFB2ILNKD3KRA24MA/bundle.json","state":"https://pith.science/pith/JZC2I3F27QFB2ILNKD3KRA24MA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JZC2I3F27QFB2ILNKD3KRA24MA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:JZC2I3F27QFB2ILNKD3KRA24MA","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":"8e08b487c473697000f778b3b48e4a1be8b4333226f5730455a4b0cd054768e8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-10-18T15:20:07Z","title_canon_sha256":"14f52c292b0bd90903f75de947596d43aaef67e85c27292535d866f8d62496ed"},"schema_version":"1.0","source":{"id":"0810.3322","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.3322","created_at":"2026-05-18T03:20:19Z"},{"alias_kind":"arxiv_version","alias_value":"0810.3322v1","created_at":"2026-05-18T03:20:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.3322","created_at":"2026-05-18T03:20:19Z"},{"alias_kind":"pith_short_12","alias_value":"JZC2I3F27QFB","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"JZC2I3F27QFB2ILN","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"JZC2I3F2","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:a4a84742c33c07a2d1618b741227714dc62d48e00fe10340ef865de55ead0652","target":"graph","created_at":"2026-05-18T03:20:19Z","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":"I show how to associate a Clifford algebra to a graph. I describe the structure of these Clifford graph algebras and provide many examples and pictures. I describe which graphs correspond to isomorphic Clifford algebras and also discuss other related sets of graphs. This construction can be used to build models of representations of simply-laced compact Lie groups.","authors_text":"Tanya Khovanova","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-10-18T15:20:07Z","title":"Clifford Algebras and Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.3322","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:a6d7355b0e0cb614cbd077294a74f939c6d58459f4b08de724f81b420f7d9763","target":"record","created_at":"2026-05-18T03:20:19Z","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":"8e08b487c473697000f778b3b48e4a1be8b4333226f5730455a4b0cd054768e8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-10-18T15:20:07Z","title_canon_sha256":"14f52c292b0bd90903f75de947596d43aaef67e85c27292535d866f8d62496ed"},"schema_version":"1.0","source":{"id":"0810.3322","kind":"arxiv","version":1}},"canonical_sha256":"4e45a46cbafc0a1d216d50f6a8835c603a66d3181011dfc92fc8ace37c990ec9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e45a46cbafc0a1d216d50f6a8835c603a66d3181011dfc92fc8ace37c990ec9","first_computed_at":"2026-05-18T03:20:19.237637Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:20:19.237637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+ePXSBKK/N42XU1ebuYIIgd8/8FUkOXGYnv6CAEg54jO9RMvdZVw3PxcXZnM946c9jXpXn7vWwmwckF+zHeYDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:20:19.238381Z","signed_message":"canonical_sha256_bytes"},"source_id":"0810.3322","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a6d7355b0e0cb614cbd077294a74f939c6d58459f4b08de724f81b420f7d9763","sha256:a4a84742c33c07a2d1618b741227714dc62d48e00fe10340ef865de55ead0652"],"state_sha256":"4a04fd3f731090b519eadc5ad8c61a7c0c674b052eed8fc6cd5e5678581fecfe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d5U2fd0vtDlDxMHCRdwJNybcgVVQqNch+qw2rFpZQPvRhx8bN2fFWtvfTRsPHZXWsI6vQpXw+GjatkixCFwPAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T14:56:13.621748Z","bundle_sha256":"09341510bbf0379bd20311aaa5eedd99b45a2c9a3b856f33bba34c0b79520c48"}}