{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:GO27RY4TUIUG2TXX37VVX6FGA2","short_pith_number":"pith:GO27RY4T","canonical_record":{"source":{"id":"1306.2797","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-12T12:12:50Z","cross_cats_sorted":[],"title_canon_sha256":"bb7867247741a3190ddbba025c2e272464664c6a265db08241386ad975e466a3","abstract_canon_sha256":"dda10c5379daa1e1fe4ce8e67df922f1ff9adf904ea26209bf5059727ace7229"},"schema_version":"1.0"},"canonical_sha256":"33b5f8e393a2286d4ef7dfeb5bf8a606a1324698bfe074c5d745e3d2f3630e09","source":{"kind":"arxiv","id":"1306.2797","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.2797","created_at":"2026-05-18T01:21:05Z"},{"alias_kind":"arxiv_version","alias_value":"1306.2797v3","created_at":"2026-05-18T01:21:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.2797","created_at":"2026-05-18T01:21:05Z"},{"alias_kind":"pith_short_12","alias_value":"GO27RY4TUIUG","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GO27RY4TUIUG2TXX","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GO27RY4T","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:GO27RY4TUIUG2TXX37VVX6FGA2","target":"record","payload":{"canonical_record":{"source":{"id":"1306.2797","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-12T12:12:50Z","cross_cats_sorted":[],"title_canon_sha256":"bb7867247741a3190ddbba025c2e272464664c6a265db08241386ad975e466a3","abstract_canon_sha256":"dda10c5379daa1e1fe4ce8e67df922f1ff9adf904ea26209bf5059727ace7229"},"schema_version":"1.0"},"canonical_sha256":"33b5f8e393a2286d4ef7dfeb5bf8a606a1324698bfe074c5d745e3d2f3630e09","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:05.616078Z","signature_b64":"qItWb8sU6jPbMWHzVzxgLgML5HGhbx6Jw/Bjcw5WbnPbRO6MfU4o+/4xz7kDnPOrLig1wQn2TWzw3v8Om1++Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"33b5f8e393a2286d4ef7dfeb5bf8a606a1324698bfe074c5d745e3d2f3630e09","last_reissued_at":"2026-05-18T01:21:05.615349Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:05.615349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.2797","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":"2026-05-18T01:21:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Us4gZyjYVxnjRiCS43GVjoz+V4gS5XaaXqwYLxA2NX1RNvpiSfYV0hzXjGvW+PJHPQsXuMISUbxEBMOg4nW3BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T20:17:53.456741Z"},"content_sha256":"28f01fcc3f42c4e2b66abb2592d9200593e9d3f7cd50c43335b30240536b1424","schema_version":"1.0","event_id":"sha256:28f01fcc3f42c4e2b66abb2592d9200593e9d3f7cd50c43335b30240536b1424"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:GO27RY4TUIUG2TXX37VVX6FGA2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantization coefficients in infinite systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Eugen Mihailescu, Mrinal Roychowdhury","submitted_at":"2013-06-12T12:12:50Z","abstract_excerpt":"We investigate quantization coefficients for self-similar probability measures \\mu on limit sets which are generated by systems S of infinitely many contractive similarities and by probabilistic vectors. The theory of quantization coefficients for infinite systems has significant differences from the finite case. One of these differences is the lack of finite maximal antichains, and the fact that the set of contraction ratios has zero infimum; another difference resides in the specific geometry of the non-compact limit set J of S. We prove that, for each r \\in (0,1), there exists a unique posi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.2797","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":"2026-05-18T01:21:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6lE3I4fFv0DRfNti0UvhlhXZG4N/IqRlTXjqm5Lrm1fvfIL4wXjiqTXmXTUNPLqzvJlFtf4kJs/ouVqlwexzBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T20:17:53.457334Z"},"content_sha256":"970b275056416a59eea2477ccfbfdd9976f36c0507c538ae31322c53aa53852d","schema_version":"1.0","event_id":"sha256:970b275056416a59eea2477ccfbfdd9976f36c0507c538ae31322c53aa53852d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GO27RY4TUIUG2TXX37VVX6FGA2/bundle.json","state_url":"https://pith.science/pith/GO27RY4TUIUG2TXX37VVX6FGA2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GO27RY4TUIUG2TXX37VVX6FGA2/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":"2026-06-30T20:17:53Z","links":{"resolver":"https://pith.science/pith/GO27RY4TUIUG2TXX37VVX6FGA2","bundle":"https://pith.science/pith/GO27RY4TUIUG2TXX37VVX6FGA2/bundle.json","state":"https://pith.science/pith/GO27RY4TUIUG2TXX37VVX6FGA2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GO27RY4TUIUG2TXX37VVX6FGA2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:GO27RY4TUIUG2TXX37VVX6FGA2","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":"dda10c5379daa1e1fe4ce8e67df922f1ff9adf904ea26209bf5059727ace7229","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-12T12:12:50Z","title_canon_sha256":"bb7867247741a3190ddbba025c2e272464664c6a265db08241386ad975e466a3"},"schema_version":"1.0","source":{"id":"1306.2797","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.2797","created_at":"2026-05-18T01:21:05Z"},{"alias_kind":"arxiv_version","alias_value":"1306.2797v3","created_at":"2026-05-18T01:21:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.2797","created_at":"2026-05-18T01:21:05Z"},{"alias_kind":"pith_short_12","alias_value":"GO27RY4TUIUG","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GO27RY4TUIUG2TXX","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GO27RY4T","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:970b275056416a59eea2477ccfbfdd9976f36c0507c538ae31322c53aa53852d","target":"graph","created_at":"2026-05-18T01:21:05Z","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 investigate quantization coefficients for self-similar probability measures \\mu on limit sets which are generated by systems S of infinitely many contractive similarities and by probabilistic vectors. The theory of quantization coefficients for infinite systems has significant differences from the finite case. One of these differences is the lack of finite maximal antichains, and the fact that the set of contraction ratios has zero infimum; another difference resides in the specific geometry of the non-compact limit set J of S. We prove that, for each r \\in (0,1), there exists a unique posi","authors_text":"Eugen Mihailescu, Mrinal Roychowdhury","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-12T12:12:50Z","title":"Quantization coefficients in infinite systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.2797","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":"sha256:28f01fcc3f42c4e2b66abb2592d9200593e9d3f7cd50c43335b30240536b1424","target":"record","created_at":"2026-05-18T01:21:05Z","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":"dda10c5379daa1e1fe4ce8e67df922f1ff9adf904ea26209bf5059727ace7229","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-12T12:12:50Z","title_canon_sha256":"bb7867247741a3190ddbba025c2e272464664c6a265db08241386ad975e466a3"},"schema_version":"1.0","source":{"id":"1306.2797","kind":"arxiv","version":3}},"canonical_sha256":"33b5f8e393a2286d4ef7dfeb5bf8a606a1324698bfe074c5d745e3d2f3630e09","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"33b5f8e393a2286d4ef7dfeb5bf8a606a1324698bfe074c5d745e3d2f3630e09","first_computed_at":"2026-05-18T01:21:05.615349Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:05.615349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qItWb8sU6jPbMWHzVzxgLgML5HGhbx6Jw/Bjcw5WbnPbRO6MfU4o+/4xz7kDnPOrLig1wQn2TWzw3v8Om1++Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:05.616078Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.2797","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28f01fcc3f42c4e2b66abb2592d9200593e9d3f7cd50c43335b30240536b1424","sha256:970b275056416a59eea2477ccfbfdd9976f36c0507c538ae31322c53aa53852d"],"state_sha256":"120440dfc4c9c3d89150604af1d68007a3005cadeed3367811ab7cbe37aee8fc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UziCHlSp2aju5/uS7drv3SgOEC58TaGufyRR1rUknhmcIbxfc/B9chMA3q7xxrBG0zB7kETVZ/HbnlyLMpjSAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T20:17:53.460247Z","bundle_sha256":"99d4018e1e973fc0f13702e6bb13ad4fd251a5b4d736523cc2caa4864cffd9f3"}}