{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:6UI6WAUINCB4NKXQHYHP7FF4VX","short_pith_number":"pith:6UI6WAUI","canonical_record":{"source":{"id":"1810.05517","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-12T13:53:37Z","cross_cats_sorted":[],"title_canon_sha256":"59441563065bea309f708f11299b302e873a91933da71a57188a53e6b6625b5a","abstract_canon_sha256":"4ffb3f805df71d368a1606fef5773a81b120d9d31d270438e92aa31956805d6e"},"schema_version":"1.0"},"canonical_sha256":"f511eb02886883c6aaf03e0eff94bcade85c5b65a67d71089ecfbd6c10bcf593","source":{"kind":"arxiv","id":"1810.05517","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.05517","created_at":"2026-05-17T23:59:38Z"},{"alias_kind":"arxiv_version","alias_value":"1810.05517v2","created_at":"2026-05-17T23:59:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.05517","created_at":"2026-05-17T23:59:38Z"},{"alias_kind":"pith_short_12","alias_value":"6UI6WAUINCB4","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6UI6WAUINCB4NKXQ","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6UI6WAUI","created_at":"2026-05-18T12:32:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:6UI6WAUINCB4NKXQHYHP7FF4VX","target":"record","payload":{"canonical_record":{"source":{"id":"1810.05517","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-12T13:53:37Z","cross_cats_sorted":[],"title_canon_sha256":"59441563065bea309f708f11299b302e873a91933da71a57188a53e6b6625b5a","abstract_canon_sha256":"4ffb3f805df71d368a1606fef5773a81b120d9d31d270438e92aa31956805d6e"},"schema_version":"1.0"},"canonical_sha256":"f511eb02886883c6aaf03e0eff94bcade85c5b65a67d71089ecfbd6c10bcf593","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:38.162144Z","signature_b64":"UuKEI74nSFEm69HF1PvsLJlC/sOxnt92Ron8KW6bgcjX6W3h0Rk1pQkEIPf7wfDLRVn8cdb+SLifqaoYKaDaAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f511eb02886883c6aaf03e0eff94bcade85c5b65a67d71089ecfbd6c10bcf593","last_reissued_at":"2026-05-17T23:59:38.161603Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:38.161603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.05517","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:59:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/G55MrCn+hFdsP/OEpMQszYxDVdlW0kROaockuL8bW/ymTBJRf7tpR+yN7rQqjoa4ZgrNk5A42/FJBYp1E/UCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T15:59:57.394523Z"},"content_sha256":"d8cbfc5c620c48ee9d7050964bcec45824b8a985a50a374643322557f477f7f5","schema_version":"1.0","event_id":"sha256:d8cbfc5c620c48ee9d7050964bcec45824b8a985a50a374643322557f477f7f5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:6UI6WAUINCB4NKXQHYHP7FF4VX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cubillages on cyclic zonotopes, membranes, and higher separatation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"A.V. Karzanov, G.A. Koshevoy, V.I. Danilov","submitted_at":"2018-10-12T13:53:37Z","abstract_excerpt":"We study certain structural properties of fine zonotopal tilings, or cubillages, on cyclic zonotopes $Z(n,d)$ of an arbitrary dimension $d$ and their relations to $(d-1)$-separated collections of subsets of a set $\\{1,2,\\ldots,n\\}$. (Collections of this sort are well known as strongly separated ones when $d=2$, and as chord separated ones when $d=3$.)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.05517","kind":"arxiv","version":2},"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":"2026-05-17T23:59:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EXKVP/0uBYNtfkMMf3K3jT2/6gOeQniGIwNHdbUIQxKloRq8ol2diPh/TPgO7+9QxyiXeCWP8KdGsubzRXJIBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T15:59:57.394862Z"},"content_sha256":"2e77e3b526509d84470daa09c8e335abe59dc1cfb974ad91e04ca3ec2085becd","schema_version":"1.0","event_id":"sha256:2e77e3b526509d84470daa09c8e335abe59dc1cfb974ad91e04ca3ec2085becd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6UI6WAUINCB4NKXQHYHP7FF4VX/bundle.json","state_url":"https://pith.science/pith/6UI6WAUINCB4NKXQHYHP7FF4VX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6UI6WAUINCB4NKXQHYHP7FF4VX/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":"2026-07-02T15:59:57Z","links":{"resolver":"https://pith.science/pith/6UI6WAUINCB4NKXQHYHP7FF4VX","bundle":"https://pith.science/pith/6UI6WAUINCB4NKXQHYHP7FF4VX/bundle.json","state":"https://pith.science/pith/6UI6WAUINCB4NKXQHYHP7FF4VX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6UI6WAUINCB4NKXQHYHP7FF4VX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6UI6WAUINCB4NKXQHYHP7FF4VX","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":"4ffb3f805df71d368a1606fef5773a81b120d9d31d270438e92aa31956805d6e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-12T13:53:37Z","title_canon_sha256":"59441563065bea309f708f11299b302e873a91933da71a57188a53e6b6625b5a"},"schema_version":"1.0","source":{"id":"1810.05517","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.05517","created_at":"2026-05-17T23:59:38Z"},{"alias_kind":"arxiv_version","alias_value":"1810.05517v2","created_at":"2026-05-17T23:59:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.05517","created_at":"2026-05-17T23:59:38Z"},{"alias_kind":"pith_short_12","alias_value":"6UI6WAUINCB4","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6UI6WAUINCB4NKXQ","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6UI6WAUI","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:2e77e3b526509d84470daa09c8e335abe59dc1cfb974ad91e04ca3ec2085becd","target":"graph","created_at":"2026-05-17T23:59:38Z","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":"We study certain structural properties of fine zonotopal tilings, or cubillages, on cyclic zonotopes $Z(n,d)$ of an arbitrary dimension $d$ and their relations to $(d-1)$-separated collections of subsets of a set $\\{1,2,\\ldots,n\\}$. (Collections of this sort are well known as strongly separated ones when $d=2$, and as chord separated ones when $d=3$.)","authors_text":"A.V. Karzanov, G.A. Koshevoy, V.I. Danilov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-12T13:53:37Z","title":"Cubillages on cyclic zonotopes, membranes, and higher separatation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.05517","kind":"arxiv","version":2},"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:d8cbfc5c620c48ee9d7050964bcec45824b8a985a50a374643322557f477f7f5","target":"record","created_at":"2026-05-17T23:59:38Z","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":"4ffb3f805df71d368a1606fef5773a81b120d9d31d270438e92aa31956805d6e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-12T13:53:37Z","title_canon_sha256":"59441563065bea309f708f11299b302e873a91933da71a57188a53e6b6625b5a"},"schema_version":"1.0","source":{"id":"1810.05517","kind":"arxiv","version":2}},"canonical_sha256":"f511eb02886883c6aaf03e0eff94bcade85c5b65a67d71089ecfbd6c10bcf593","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f511eb02886883c6aaf03e0eff94bcade85c5b65a67d71089ecfbd6c10bcf593","first_computed_at":"2026-05-17T23:59:38.161603Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:38.161603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UuKEI74nSFEm69HF1PvsLJlC/sOxnt92Ron8KW6bgcjX6W3h0Rk1pQkEIPf7wfDLRVn8cdb+SLifqaoYKaDaAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:38.162144Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.05517","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d8cbfc5c620c48ee9d7050964bcec45824b8a985a50a374643322557f477f7f5","sha256:2e77e3b526509d84470daa09c8e335abe59dc1cfb974ad91e04ca3ec2085becd"],"state_sha256":"a21d54a3feb6bb49a5affb98d8ce35471747e54598ca4955e7ead1a359941d86"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vRLgcyzZ7Fcqtur7wVcB7/Jv75eSMLPQFzUWsqZBWpBYmXTQ4/FsOY0xAwd686X7c8q8fp81Hoot6uJCgd9kAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T15:59:57.396632Z","bundle_sha256":"6059d5f1c63696079ab1b23ede686fc5cf1d597658e52a7cf5a4a2acfcfd9128"}}