{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:VKD6ZPYEIAQU3NGHE2K6UR4PB6","short_pith_number":"pith:VKD6ZPYE","canonical_record":{"source":{"id":"1704.05758","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-04-19T14:52:39Z","cross_cats_sorted":["math.IT","math.PR"],"title_canon_sha256":"7bcae70530f44ccae6a97645f01eb3ccc5aaca39b23dfa6766dd1161038ff0c0","abstract_canon_sha256":"534724bab0a3bfd28f46e52f2221cf63293cf5f7de63f68cad33b39bb5a7a70d"},"schema_version":"1.0"},"canonical_sha256":"aa87ecbf0440214db4c72695ea478f0f870363af112d55dc25b56c7001deb0f0","source":{"kind":"arxiv","id":"1704.05758","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.05758","created_at":"2026-05-18T00:15:30Z"},{"alias_kind":"arxiv_version","alias_value":"1704.05758v2","created_at":"2026-05-18T00:15:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.05758","created_at":"2026-05-18T00:15:30Z"},{"alias_kind":"pith_short_12","alias_value":"VKD6ZPYEIAQU","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VKD6ZPYEIAQU3NGH","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VKD6ZPYE","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:VKD6ZPYEIAQU3NGHE2K6UR4PB6","target":"record","payload":{"canonical_record":{"source":{"id":"1704.05758","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-04-19T14:52:39Z","cross_cats_sorted":["math.IT","math.PR"],"title_canon_sha256":"7bcae70530f44ccae6a97645f01eb3ccc5aaca39b23dfa6766dd1161038ff0c0","abstract_canon_sha256":"534724bab0a3bfd28f46e52f2221cf63293cf5f7de63f68cad33b39bb5a7a70d"},"schema_version":"1.0"},"canonical_sha256":"aa87ecbf0440214db4c72695ea478f0f870363af112d55dc25b56c7001deb0f0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:30.790706Z","signature_b64":"p24rH2WWZN+8R0QP4tah/z/7P+bhZwP82ao1vVStdMF6+qyMIt5o14MIKr0Zi9mffUVIIQxpUJQGQysKZpMnBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa87ecbf0440214db4c72695ea478f0f870363af112d55dc25b56c7001deb0f0","last_reissued_at":"2026-05-18T00:15:30.790201Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:30.790201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.05758","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":"2026-05-18T00:15:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"18hQqk4IxhVHvQ24gWWzUU1gZPKeHVLLaGu/+dn7HErYFjvSkY3Z7IBFi0QVABkrKOjxAwBWsXU3tg6aW6T9AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T18:26:09.695930Z"},"content_sha256":"9f39a4f754e7184d60daab0aaeb1df253f4170a870dfaf903fe2ec4e255a687e","schema_version":"1.0","event_id":"sha256:9f39a4f754e7184d60daab0aaeb1df253f4170a870dfaf903fe2ec4e255a687e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:VKD6ZPYEIAQU3NGHE2K6UR4PB6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rate-Distortion Theory of Finite Point Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.PR"],"primary_cat":"cs.IT","authors_text":"Dominic Schuhmacher, Franz Hlawatsch, G\\\"unther Koliander","submitted_at":"2017-04-19T14:52:39Z","abstract_excerpt":"We study the compression of data in the case where the useful information is contained in a set rather than a vector, i.e., the ordering of the data points is irrelevant and the number of data points is unknown. Our analysis is based on rate-distortion theory and the theory of finite point processes. We introduce fundamental information-theoretic concepts and quantities for point processes and present general lower and upper bounds on the rate-distortion function. To enable a comparison with the vector setting, we concretize our bounds for point processes of fixed cardinality. In particular, w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05758","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":"2026-05-18T00:15:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U7T4k1AXrp5LYm5PkZDzVXEZ8FmnklIUdanagP8XaO9bUtZ5gsCf8cRaHAhkyHH+QwQxu1bPejqIdMf4NWLvAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T18:26:09.696635Z"},"content_sha256":"f7496c592de5ffa1b8115099dfa59abf1ca18a5c2c01f2ac9077a7902a380421","schema_version":"1.0","event_id":"sha256:f7496c592de5ffa1b8115099dfa59abf1ca18a5c2c01f2ac9077a7902a380421"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VKD6ZPYEIAQU3NGHE2K6UR4PB6/bundle.json","state_url":"https://pith.science/pith/VKD6ZPYEIAQU3NGHE2K6UR4PB6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VKD6ZPYEIAQU3NGHE2K6UR4PB6/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":"2026-05-29T18:26:09Z","links":{"resolver":"https://pith.science/pith/VKD6ZPYEIAQU3NGHE2K6UR4PB6","bundle":"https://pith.science/pith/VKD6ZPYEIAQU3NGHE2K6UR4PB6/bundle.json","state":"https://pith.science/pith/VKD6ZPYEIAQU3NGHE2K6UR4PB6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VKD6ZPYEIAQU3NGHE2K6UR4PB6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VKD6ZPYEIAQU3NGHE2K6UR4PB6","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":"534724bab0a3bfd28f46e52f2221cf63293cf5f7de63f68cad33b39bb5a7a70d","cross_cats_sorted":["math.IT","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-04-19T14:52:39Z","title_canon_sha256":"7bcae70530f44ccae6a97645f01eb3ccc5aaca39b23dfa6766dd1161038ff0c0"},"schema_version":"1.0","source":{"id":"1704.05758","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.05758","created_at":"2026-05-18T00:15:30Z"},{"alias_kind":"arxiv_version","alias_value":"1704.05758v2","created_at":"2026-05-18T00:15:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.05758","created_at":"2026-05-18T00:15:30Z"},{"alias_kind":"pith_short_12","alias_value":"VKD6ZPYEIAQU","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VKD6ZPYEIAQU3NGH","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VKD6ZPYE","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:f7496c592de5ffa1b8115099dfa59abf1ca18a5c2c01f2ac9077a7902a380421","target":"graph","created_at":"2026-05-18T00:15:30Z","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 the compression of data in the case where the useful information is contained in a set rather than a vector, i.e., the ordering of the data points is irrelevant and the number of data points is unknown. Our analysis is based on rate-distortion theory and the theory of finite point processes. We introduce fundamental information-theoretic concepts and quantities for point processes and present general lower and upper bounds on the rate-distortion function. To enable a comparison with the vector setting, we concretize our bounds for point processes of fixed cardinality. In particular, w","authors_text":"Dominic Schuhmacher, Franz Hlawatsch, G\\\"unther Koliander","cross_cats":["math.IT","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-04-19T14:52:39Z","title":"Rate-Distortion Theory of Finite Point Processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05758","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":"sha256:9f39a4f754e7184d60daab0aaeb1df253f4170a870dfaf903fe2ec4e255a687e","target":"record","created_at":"2026-05-18T00:15:30Z","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":"534724bab0a3bfd28f46e52f2221cf63293cf5f7de63f68cad33b39bb5a7a70d","cross_cats_sorted":["math.IT","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-04-19T14:52:39Z","title_canon_sha256":"7bcae70530f44ccae6a97645f01eb3ccc5aaca39b23dfa6766dd1161038ff0c0"},"schema_version":"1.0","source":{"id":"1704.05758","kind":"arxiv","version":2}},"canonical_sha256":"aa87ecbf0440214db4c72695ea478f0f870363af112d55dc25b56c7001deb0f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aa87ecbf0440214db4c72695ea478f0f870363af112d55dc25b56c7001deb0f0","first_computed_at":"2026-05-18T00:15:30.790201Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:30.790201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p24rH2WWZN+8R0QP4tah/z/7P+bhZwP82ao1vVStdMF6+qyMIt5o14MIKr0Zi9mffUVIIQxpUJQGQysKZpMnBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:30.790706Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.05758","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9f39a4f754e7184d60daab0aaeb1df253f4170a870dfaf903fe2ec4e255a687e","sha256:f7496c592de5ffa1b8115099dfa59abf1ca18a5c2c01f2ac9077a7902a380421"],"state_sha256":"4892f31ed8b10cb0318953d410d27ab35334919d44c96fc71d32f04f38e493d5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NpS2NG0Rq1w7nQzQDPlhnXlIC/EXQ2Bb6vAdbh2yf+wIE6N68RNttMzerQAG7vf3Ga28GcmumOnf2NzSMZsMCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T18:26:09.700149Z","bundle_sha256":"b3d8cbe16245e21567dbffe364907152776a9d2fa8456992884f3270fa3f8be3"}}