{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:XR643PSVOZYTDAVKLLZWVFLKON","short_pith_number":"pith:XR643PSV","canonical_record":{"source":{"id":"1301.3484","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-01-15T20:47:35Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"d23a5027f6ed93bf717b6893554b1e4bda73cc2faa83c717619894b32af9f025","abstract_canon_sha256":"b7610af8a429550a7fc22a0d8a3814980a4a42a27415d1cd18f30e7897e271b9"},"schema_version":"1.0"},"canonical_sha256":"bc7dcdbe5576713182aa5af36a956a7365fade84305c197c08565408bf9242df","source":{"kind":"arxiv","id":"1301.3484","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.3484","created_at":"2026-05-18T00:47:21Z"},{"alias_kind":"arxiv_version","alias_value":"1301.3484v3","created_at":"2026-05-18T00:47:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.3484","created_at":"2026-05-18T00:47:21Z"},{"alias_kind":"pith_short_12","alias_value":"XR643PSVOZYT","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XR643PSVOZYTDAVK","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XR643PSV","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:XR643PSVOZYTDAVKLLZWVFLKON","target":"record","payload":{"canonical_record":{"source":{"id":"1301.3484","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-01-15T20:47:35Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"d23a5027f6ed93bf717b6893554b1e4bda73cc2faa83c717619894b32af9f025","abstract_canon_sha256":"b7610af8a429550a7fc22a0d8a3814980a4a42a27415d1cd18f30e7897e271b9"},"schema_version":"1.0"},"canonical_sha256":"bc7dcdbe5576713182aa5af36a956a7365fade84305c197c08565408bf9242df","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:21.469131Z","signature_b64":"RkEr77xQsS9ZQiWHysyeDwh/sNFmKAAikW2W+vsp/nXDdcKxdx7QBqKDUDb1RN/qM4qg8jefHmiEp/a5OK4ODA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc7dcdbe5576713182aa5af36a956a7365fade84305c197c08565408bf9242df","last_reissued_at":"2026-05-18T00:47:21.468532Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:21.468532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.3484","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:47:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8nfJUPTz2q/x8s9vGD33VbKpL7Zeqzgk75XR4vgNczlk/vZGNDTlvwQ5oLS+ABHRB1uNn6wzcQvQ16FklZNhAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T14:12:49.340474Z"},"content_sha256":"22fc6e0f7fb3a3ba252a173505327a8668c91a8a48aee26d7d41047598b26de7","schema_version":"1.0","event_id":"sha256:22fc6e0f7fb3a3ba252a173505327a8668c91a8a48aee26d7d41047598b26de7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:XR643PSVOZYTDAVKLLZWVFLKON","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic dimension, decomposition complexity, and Haver's property C","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.MG","authors_text":"Alexander Dranishnikov, Michael Zarichnyi","submitted_at":"2013-01-15T20:47:35Z","abstract_excerpt":"The notion of the decomposition complexity was introduced in \\cite{GTY} using a game theoretical approach. We introduce a notion of straight decomposition complexity and compare it with the original as well with the asymptotic property C. Then we define a game theoretical analog of Haver's property C in the classical dimension theory and compare it with the original."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.3484","kind":"arxiv","version":3},"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":"2026-05-18T00:47:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y4g03Q8E9/4jfh1PxJWktXhneTUv85Hvclr9ZoRLcDQPFBrPpWwa/wSSY05GIHlFDvCVPOul4EpzfkYq0+7xBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T14:12:49.341114Z"},"content_sha256":"c9cac90d1e8183d3f37d42f33c2951e8fe18e1af81dc341cc31fe6e8b3ee6c47","schema_version":"1.0","event_id":"sha256:c9cac90d1e8183d3f37d42f33c2951e8fe18e1af81dc341cc31fe6e8b3ee6c47"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XR643PSVOZYTDAVKLLZWVFLKON/bundle.json","state_url":"https://pith.science/pith/XR643PSVOZYTDAVKLLZWVFLKON/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XR643PSVOZYTDAVKLLZWVFLKON/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":"2026-06-06T14:12:49Z","links":{"resolver":"https://pith.science/pith/XR643PSVOZYTDAVKLLZWVFLKON","bundle":"https://pith.science/pith/XR643PSVOZYTDAVKLLZWVFLKON/bundle.json","state":"https://pith.science/pith/XR643PSVOZYTDAVKLLZWVFLKON/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XR643PSVOZYTDAVKLLZWVFLKON/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XR643PSVOZYTDAVKLLZWVFLKON","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":"b7610af8a429550a7fc22a0d8a3814980a4a42a27415d1cd18f30e7897e271b9","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-01-15T20:47:35Z","title_canon_sha256":"d23a5027f6ed93bf717b6893554b1e4bda73cc2faa83c717619894b32af9f025"},"schema_version":"1.0","source":{"id":"1301.3484","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.3484","created_at":"2026-05-18T00:47:21Z"},{"alias_kind":"arxiv_version","alias_value":"1301.3484v3","created_at":"2026-05-18T00:47:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.3484","created_at":"2026-05-18T00:47:21Z"},{"alias_kind":"pith_short_12","alias_value":"XR643PSVOZYT","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XR643PSVOZYTDAVK","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XR643PSV","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:c9cac90d1e8183d3f37d42f33c2951e8fe18e1af81dc341cc31fe6e8b3ee6c47","target":"graph","created_at":"2026-05-18T00:47:21Z","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 notion of the decomposition complexity was introduced in \\cite{GTY} using a game theoretical approach. We introduce a notion of straight decomposition complexity and compare it with the original as well with the asymptotic property C. Then we define a game theoretical analog of Haver's property C in the classical dimension theory and compare it with the original.","authors_text":"Alexander Dranishnikov, Michael Zarichnyi","cross_cats":["math.GN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-01-15T20:47:35Z","title":"Asymptotic dimension, decomposition complexity, and Haver's property C"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.3484","kind":"arxiv","version":3},"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":"sha256:22fc6e0f7fb3a3ba252a173505327a8668c91a8a48aee26d7d41047598b26de7","target":"record","created_at":"2026-05-18T00:47:21Z","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":"b7610af8a429550a7fc22a0d8a3814980a4a42a27415d1cd18f30e7897e271b9","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-01-15T20:47:35Z","title_canon_sha256":"d23a5027f6ed93bf717b6893554b1e4bda73cc2faa83c717619894b32af9f025"},"schema_version":"1.0","source":{"id":"1301.3484","kind":"arxiv","version":3}},"canonical_sha256":"bc7dcdbe5576713182aa5af36a956a7365fade84305c197c08565408bf9242df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc7dcdbe5576713182aa5af36a956a7365fade84305c197c08565408bf9242df","first_computed_at":"2026-05-18T00:47:21.468532Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:21.468532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RkEr77xQsS9ZQiWHysyeDwh/sNFmKAAikW2W+vsp/nXDdcKxdx7QBqKDUDb1RN/qM4qg8jefHmiEp/a5OK4ODA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:21.469131Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.3484","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:22fc6e0f7fb3a3ba252a173505327a8668c91a8a48aee26d7d41047598b26de7","sha256:c9cac90d1e8183d3f37d42f33c2951e8fe18e1af81dc341cc31fe6e8b3ee6c47"],"state_sha256":"0c8b2abc7ab8ff46d7466b751239504331fe09a60a9bd980e5f0ef45c58e9947"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y4x9JBqHw7s3jGksy/IloQJpsgXLqESfy66BU9l1s+M1jh+xtWtb3o3R47MvO0DiQI8C4a+BCeY5mIEHPUqWAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T14:12:49.346075Z","bundle_sha256":"95ce6327f07d2194c67f617ef9dcd063af81f1b8b04c544afafb275c3af9067f"}}