{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:GGRCZFU77SZYPT7HXYRM74V65E","short_pith_number":"pith:GGRCZFU7","canonical_record":{"source":{"id":"2606.29373","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2026-06-28T12:38:54Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"20a5649fe87d8e0d680dfaa7653ffc061163312c0c7cf1a59d8d20e401091c3b","abstract_canon_sha256":"a279f7dd6750cfe236a59489d2cf23d07022f32ddc4bbda97cb894eb3d6856a5"},"schema_version":"1.0"},"canonical_sha256":"31a22c969ffcb387cfe7be22cff2bee92d25dbb0ddafc295ae9d8d4000c75324","source":{"kind":"arxiv","id":"2606.29373","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.29373","created_at":"2026-06-30T01:18:03Z"},{"alias_kind":"arxiv_version","alias_value":"2606.29373v1","created_at":"2026-06-30T01:18:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.29373","created_at":"2026-06-30T01:18:03Z"},{"alias_kind":"pith_short_12","alias_value":"GGRCZFU77SZY","created_at":"2026-06-30T01:18:03Z"},{"alias_kind":"pith_short_16","alias_value":"GGRCZFU77SZYPT7H","created_at":"2026-06-30T01:18:03Z"},{"alias_kind":"pith_short_8","alias_value":"GGRCZFU7","created_at":"2026-06-30T01:18:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:GGRCZFU77SZYPT7HXYRM74V65E","target":"record","payload":{"canonical_record":{"source":{"id":"2606.29373","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2026-06-28T12:38:54Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"20a5649fe87d8e0d680dfaa7653ffc061163312c0c7cf1a59d8d20e401091c3b","abstract_canon_sha256":"a279f7dd6750cfe236a59489d2cf23d07022f32ddc4bbda97cb894eb3d6856a5"},"schema_version":"1.0"},"canonical_sha256":"31a22c969ffcb387cfe7be22cff2bee92d25dbb0ddafc295ae9d8d4000c75324","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T01:18:03.326843Z","signature_b64":"H0l2rQyKmbQPo+NMrKQcK+KHKyGGnnIV/SDWejKBgX2meRG1WU+4Sif8sID47cA//wPSMmeJ7iwk50qV3CJFAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31a22c969ffcb387cfe7be22cff2bee92d25dbb0ddafc295ae9d8d4000c75324","last_reissued_at":"2026-06-30T01:18:03.326372Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T01:18:03.326372Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.29373","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":"2026-06-30T01:18:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xy2E3j6/veAfyFmbE+fLABvmh4h6XLCvAFj9ggfvBL+87YLualGwEQeP1w6v9V+Tsxwlw+XE5d2lBA474KQUAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T06:35:42.916886Z"},"content_sha256":"5810825e54cc6e6525b313a44206d5a8a45180a680e6193d5aa4af38d846efa7","schema_version":"1.0","event_id":"sha256:5810825e54cc6e6525b313a44206d5a8a45180a680e6193d5aa4af38d846efa7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:GGRCZFU77SZYPT7HXYRM74V65E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Oriented Street--Roberts Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.AT","authors_text":"David Gepner, Hadrian Heine","submitted_at":"2026-06-28T12:38:54Z","abstract_excerpt":"We formulate a notion of oriented polytope, including Street's oriented simplices and Gray's oriented cubes, and use this to prove an oriented version of the Street--Roberts conjecture, presenting $(\\infty,\\infty)$-categories as sheaves on suitable families of oriented polytopes, generalizing work of Campion. This allows us to understand $(\\infty, \\infty)$-categories from a geometric perspective, as directed analogues of homotopy types. These familes of oriented polytopes induce basic operations in higher category theory: for instance, the join, Gray tensor, and bicone arise from the geometry "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.29373","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.29373/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":"2026-06-30T01:18:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fL3IoUDNrkamPzT+VGomCxTMYWlsba+yKAuEYf0yX7mAanhisC3BsvbZOg8MEnOh0iXV39itENbhaMt++/liBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T06:35:42.917371Z"},"content_sha256":"c8a570a346e9f4e1f64067761d9b60852cf5a532f2864a0246b06d8b58439038","schema_version":"1.0","event_id":"sha256:c8a570a346e9f4e1f64067761d9b60852cf5a532f2864a0246b06d8b58439038"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GGRCZFU77SZYPT7HXYRM74V65E/bundle.json","state_url":"https://pith.science/pith/GGRCZFU77SZYPT7HXYRM74V65E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GGRCZFU77SZYPT7HXYRM74V65E/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":"2026-06-30T06:35:42Z","links":{"resolver":"https://pith.science/pith/GGRCZFU77SZYPT7HXYRM74V65E","bundle":"https://pith.science/pith/GGRCZFU77SZYPT7HXYRM74V65E/bundle.json","state":"https://pith.science/pith/GGRCZFU77SZYPT7HXYRM74V65E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GGRCZFU77SZYPT7HXYRM74V65E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:GGRCZFU77SZYPT7HXYRM74V65E","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":"a279f7dd6750cfe236a59489d2cf23d07022f32ddc4bbda97cb894eb3d6856a5","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2026-06-28T12:38:54Z","title_canon_sha256":"20a5649fe87d8e0d680dfaa7653ffc061163312c0c7cf1a59d8d20e401091c3b"},"schema_version":"1.0","source":{"id":"2606.29373","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.29373","created_at":"2026-06-30T01:18:03Z"},{"alias_kind":"arxiv_version","alias_value":"2606.29373v1","created_at":"2026-06-30T01:18:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.29373","created_at":"2026-06-30T01:18:03Z"},{"alias_kind":"pith_short_12","alias_value":"GGRCZFU77SZY","created_at":"2026-06-30T01:18:03Z"},{"alias_kind":"pith_short_16","alias_value":"GGRCZFU77SZYPT7H","created_at":"2026-06-30T01:18:03Z"},{"alias_kind":"pith_short_8","alias_value":"GGRCZFU7","created_at":"2026-06-30T01:18:03Z"}],"graph_snapshots":[{"event_id":"sha256:c8a570a346e9f4e1f64067761d9b60852cf5a532f2864a0246b06d8b58439038","target":"graph","created_at":"2026-06-30T01:18:03Z","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/2606.29373/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We formulate a notion of oriented polytope, including Street's oriented simplices and Gray's oriented cubes, and use this to prove an oriented version of the Street--Roberts conjecture, presenting $(\\infty,\\infty)$-categories as sheaves on suitable families of oriented polytopes, generalizing work of Campion. This allows us to understand $(\\infty, \\infty)$-categories from a geometric perspective, as directed analogues of homotopy types. These familes of oriented polytopes induce basic operations in higher category theory: for instance, the join, Gray tensor, and bicone arise from the geometry ","authors_text":"David Gepner, Hadrian Heine","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2026-06-28T12:38:54Z","title":"An Oriented Street--Roberts Conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.29373","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":"sha256:5810825e54cc6e6525b313a44206d5a8a45180a680e6193d5aa4af38d846efa7","target":"record","created_at":"2026-06-30T01:18:03Z","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":"a279f7dd6750cfe236a59489d2cf23d07022f32ddc4bbda97cb894eb3d6856a5","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2026-06-28T12:38:54Z","title_canon_sha256":"20a5649fe87d8e0d680dfaa7653ffc061163312c0c7cf1a59d8d20e401091c3b"},"schema_version":"1.0","source":{"id":"2606.29373","kind":"arxiv","version":1}},"canonical_sha256":"31a22c969ffcb387cfe7be22cff2bee92d25dbb0ddafc295ae9d8d4000c75324","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31a22c969ffcb387cfe7be22cff2bee92d25dbb0ddafc295ae9d8d4000c75324","first_computed_at":"2026-06-30T01:18:03.326372Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-30T01:18:03.326372Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H0l2rQyKmbQPo+NMrKQcK+KHKyGGnnIV/SDWejKBgX2meRG1WU+4Sif8sID47cA//wPSMmeJ7iwk50qV3CJFAQ==","signature_status":"signed_v1","signed_at":"2026-06-30T01:18:03.326843Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.29373","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5810825e54cc6e6525b313a44206d5a8a45180a680e6193d5aa4af38d846efa7","sha256:c8a570a346e9f4e1f64067761d9b60852cf5a532f2864a0246b06d8b58439038"],"state_sha256":"3ff8d1a86a3e40e2bc5daba6e61425165016235679d9b2d8a832a7fb54ee5a63"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hK1OnPYHWSTE7cbPZmsSdu/XrnFEVsEi0pliYXtX0GPncTW0D99m+AplBcCgjD+Ym+kdFBHnVqo7fvoHaCB0Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T06:35:42.919866Z","bundle_sha256":"e26cd753d852a48252d0ff3eaca1a2ad5e5669b51df377864f0ffdcc1650d85b"}}