{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:HAJGIO6VQ3YDNM3LLK4HPQGC3F","short_pith_number":"pith:HAJGIO6V","canonical_record":{"source":{"id":"1602.05073","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-02-16T16:15:19Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"75a465ab13abe1b675ea7950dbf809bb84f96875159e621053d343fa4e3336d3","abstract_canon_sha256":"b27a6c4e9744346b67aa9f72f83cefa5f358d6bc6d4e3db40ff76c93bf3c2c94"},"schema_version":"1.0"},"canonical_sha256":"3812643bd586f036b36b5ab877c0c2d94679627ff17cc6281be1f989af983394","source":{"kind":"arxiv","id":"1602.05073","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.05073","created_at":"2026-05-18T01:20:37Z"},{"alias_kind":"arxiv_version","alias_value":"1602.05073v1","created_at":"2026-05-18T01:20:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.05073","created_at":"2026-05-18T01:20:37Z"},{"alias_kind":"pith_short_12","alias_value":"HAJGIO6VQ3YD","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HAJGIO6VQ3YDNM3L","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HAJGIO6V","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:HAJGIO6VQ3YDNM3LLK4HPQGC3F","target":"record","payload":{"canonical_record":{"source":{"id":"1602.05073","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-02-16T16:15:19Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"75a465ab13abe1b675ea7950dbf809bb84f96875159e621053d343fa4e3336d3","abstract_canon_sha256":"b27a6c4e9744346b67aa9f72f83cefa5f358d6bc6d4e3db40ff76c93bf3c2c94"},"schema_version":"1.0"},"canonical_sha256":"3812643bd586f036b36b5ab877c0c2d94679627ff17cc6281be1f989af983394","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:37.581136Z","signature_b64":"e0Ce1exD+VjxslGG/2kqD/lC0hYDZJSzrZAVbk19IwLepUukYkgHQXQfqcer7XPXevOKZK6+cykbcl3i2w9MBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3812643bd586f036b36b5ab877c0c2d94679627ff17cc6281be1f989af983394","last_reissued_at":"2026-05-18T01:20:37.580696Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:37.580696Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.05073","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":"2026-05-18T01:20:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"34lw950pUzS7lgdDYov7bPNES3ksNRou+bgdqpetfu/PTEm30PfB12bPJU5+3n/sZzGLc7ebm1E09Nox5Yo7Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T14:19:40.907480Z"},"content_sha256":"649d827c35c2d1bb8c43f902022f6bf2fe2bb19cfb41f3484094d8913b90de64","schema_version":"1.0","event_id":"sha256:649d827c35c2d1bb8c43f902022f6bf2fe2bb19cfb41f3484094d8913b90de64"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:HAJGIO6VQ3YDNM3LLK4HPQGC3F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dependence of the heavily covered point on parameters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.MG","authors_text":"Alexey Balitskiy, Roman Karasev","submitted_at":"2016-02-16T16:15:19Z","abstract_excerpt":"We examine Gromov's method of selecting a point \"heavily covered\" by simplices formed by a given finite point sets, in order to understand the dependence of the heavily covered point on parameters. We have no continuous dependence, but manage to utilize the \"homological continuous dependence\" of the heavily covered point. This allows us to infer some corollaries in a usual way. We also give an elementary argument to prove the simplest of these corollaries."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05073","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":"2026-05-18T01:20:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KB5+z/4BwfZsh9PQjrpJrvUPCzGr6wCierb5vuKzMjb5ZQ09uG8HrO/FsvBr0wc9FPW0RaI8pITcydIhXjqFCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T14:19:40.907951Z"},"content_sha256":"b54af5d08f389b2902b1f05d147fb464bf2f9c3df61892140bfb3dcda928978c","schema_version":"1.0","event_id":"sha256:b54af5d08f389b2902b1f05d147fb464bf2f9c3df61892140bfb3dcda928978c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HAJGIO6VQ3YDNM3LLK4HPQGC3F/bundle.json","state_url":"https://pith.science/pith/HAJGIO6VQ3YDNM3LLK4HPQGC3F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HAJGIO6VQ3YDNM3LLK4HPQGC3F/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":"2026-05-22T14:19:40Z","links":{"resolver":"https://pith.science/pith/HAJGIO6VQ3YDNM3LLK4HPQGC3F","bundle":"https://pith.science/pith/HAJGIO6VQ3YDNM3LLK4HPQGC3F/bundle.json","state":"https://pith.science/pith/HAJGIO6VQ3YDNM3LLK4HPQGC3F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HAJGIO6VQ3YDNM3LLK4HPQGC3F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:HAJGIO6VQ3YDNM3LLK4HPQGC3F","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":"b27a6c4e9744346b67aa9f72f83cefa5f358d6bc6d4e3db40ff76c93bf3c2c94","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-02-16T16:15:19Z","title_canon_sha256":"75a465ab13abe1b675ea7950dbf809bb84f96875159e621053d343fa4e3336d3"},"schema_version":"1.0","source":{"id":"1602.05073","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.05073","created_at":"2026-05-18T01:20:37Z"},{"alias_kind":"arxiv_version","alias_value":"1602.05073v1","created_at":"2026-05-18T01:20:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.05073","created_at":"2026-05-18T01:20:37Z"},{"alias_kind":"pith_short_12","alias_value":"HAJGIO6VQ3YD","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HAJGIO6VQ3YDNM3L","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HAJGIO6V","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:b54af5d08f389b2902b1f05d147fb464bf2f9c3df61892140bfb3dcda928978c","target":"graph","created_at":"2026-05-18T01:20:37Z","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 examine Gromov's method of selecting a point \"heavily covered\" by simplices formed by a given finite point sets, in order to understand the dependence of the heavily covered point on parameters. We have no continuous dependence, but manage to utilize the \"homological continuous dependence\" of the heavily covered point. This allows us to infer some corollaries in a usual way. We also give an elementary argument to prove the simplest of these corollaries.","authors_text":"Alexey Balitskiy, Roman Karasev","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-02-16T16:15:19Z","title":"Dependence of the heavily covered point on parameters"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05073","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":"sha256:649d827c35c2d1bb8c43f902022f6bf2fe2bb19cfb41f3484094d8913b90de64","target":"record","created_at":"2026-05-18T01:20:37Z","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":"b27a6c4e9744346b67aa9f72f83cefa5f358d6bc6d4e3db40ff76c93bf3c2c94","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-02-16T16:15:19Z","title_canon_sha256":"75a465ab13abe1b675ea7950dbf809bb84f96875159e621053d343fa4e3336d3"},"schema_version":"1.0","source":{"id":"1602.05073","kind":"arxiv","version":1}},"canonical_sha256":"3812643bd586f036b36b5ab877c0c2d94679627ff17cc6281be1f989af983394","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3812643bd586f036b36b5ab877c0c2d94679627ff17cc6281be1f989af983394","first_computed_at":"2026-05-18T01:20:37.580696Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:37.580696Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e0Ce1exD+VjxslGG/2kqD/lC0hYDZJSzrZAVbk19IwLepUukYkgHQXQfqcer7XPXevOKZK6+cykbcl3i2w9MBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:37.581136Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.05073","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:649d827c35c2d1bb8c43f902022f6bf2fe2bb19cfb41f3484094d8913b90de64","sha256:b54af5d08f389b2902b1f05d147fb464bf2f9c3df61892140bfb3dcda928978c"],"state_sha256":"ba8a89b13e60019e0ba650d44d34d3fb2a384618bd2ba4ad153e8c4bd47ab739"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eqpCWaGJyrrMCZ8wMoIJAT4yl7Cf/rfA6GsP+roA1DKP9ncU+qqZuIMWltOXQ10I8EpkGK7RfZOdek9Gz4P3CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T14:19:40.911604Z","bundle_sha256":"61b79945f41af0644800ec2ffbef7f60f384829b15685652cedae47b85bd27c7"}}