{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:W5XYZZS4FE2O4L66IFBUUFZAVA","short_pith_number":"pith:W5XYZZS4","canonical_record":{"source":{"id":"1401.5969","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-01-23T13:40:55Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"c3c2ca1bc202fa86a9dc5d6e7f7f93fbb86409c7e0e6de388c349183796b5c0b","abstract_canon_sha256":"3175023d8f9fcbbd020755f4632a9cc2b2ae73a3f56a2f477ccecae4d074c5b2"},"schema_version":"1.0"},"canonical_sha256":"b76f8ce65c2934ee2fde41434a1720a80a59bb820d426c18d489b383e941c177","source":{"kind":"arxiv","id":"1401.5969","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.5969","created_at":"2026-05-18T00:24:45Z"},{"alias_kind":"arxiv_version","alias_value":"1401.5969v3","created_at":"2026-05-18T00:24:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.5969","created_at":"2026-05-18T00:24:45Z"},{"alias_kind":"pith_short_12","alias_value":"W5XYZZS4FE2O","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"W5XYZZS4FE2O4L66","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"W5XYZZS4","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:W5XYZZS4FE2O4L66IFBUUFZAVA","target":"record","payload":{"canonical_record":{"source":{"id":"1401.5969","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-01-23T13:40:55Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"c3c2ca1bc202fa86a9dc5d6e7f7f93fbb86409c7e0e6de388c349183796b5c0b","abstract_canon_sha256":"3175023d8f9fcbbd020755f4632a9cc2b2ae73a3f56a2f477ccecae4d074c5b2"},"schema_version":"1.0"},"canonical_sha256":"b76f8ce65c2934ee2fde41434a1720a80a59bb820d426c18d489b383e941c177","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:45.685019Z","signature_b64":"FEu4YC4KlCMcAxjaaUBwZl9VxT7QP8+fhd7kJI2QOR55Su3QRkLJNb80XQwlqtWzwA3bS2vxmfbfC+R3tslqAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b76f8ce65c2934ee2fde41434a1720a80a59bb820d426c18d489b383e941c177","last_reissued_at":"2026-05-18T00:24:45.684527Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:45.684527Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.5969","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":"2026-05-18T00:24:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6emJlnAp8D3Blj30dRMmB9c5dLBdne/JkT3A8k1OQsKMGzob5REeWL9cjN5Ip6LZmM76GpHdk7vvRK0zx9IrBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T11:43:06.329201Z"},"content_sha256":"5ab99ea615c4e0054ea1ad3f78dcb144c3444b77c31e9452457e1ea2a9d94fae","schema_version":"1.0","event_id":"sha256:5ab99ea615c4e0054ea1ad3f78dcb144c3444b77c31e9452457e1ea2a9d94fae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:W5XYZZS4FE2O4L66IFBUUFZAVA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Entropy of subordinate shift spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.DS","authors_text":"Dominik Kwietniak, Jian Li, Marcin Kulczycki","submitted_at":"2014-01-23T13:40:55Z","abstract_excerpt":"We introduce a new family of shift spaces --- the subordinate shifts. Using subordinate shifts we prove in an elementary way that for every nonnegative real number $t$ there is a shift space with entropy $t$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.5969","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":"2026-05-18T00:24:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5X9wTi06ENCjE+WHs03k+OKh6ljiM/3o0UkS1Kr8fLKrCWInqUMKcVLbRkZ2VcSIHD2j5AWMd6Sp4Ss+gflcCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T11:43:06.329549Z"},"content_sha256":"53bb9f5331bd1bbfcaf46a2f2383874d5ecf42902741811861debf80609b1c7c","schema_version":"1.0","event_id":"sha256:53bb9f5331bd1bbfcaf46a2f2383874d5ecf42902741811861debf80609b1c7c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W5XYZZS4FE2O4L66IFBUUFZAVA/bundle.json","state_url":"https://pith.science/pith/W5XYZZS4FE2O4L66IFBUUFZAVA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W5XYZZS4FE2O4L66IFBUUFZAVA/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":"2026-06-05T11:43:06Z","links":{"resolver":"https://pith.science/pith/W5XYZZS4FE2O4L66IFBUUFZAVA","bundle":"https://pith.science/pith/W5XYZZS4FE2O4L66IFBUUFZAVA/bundle.json","state":"https://pith.science/pith/W5XYZZS4FE2O4L66IFBUUFZAVA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W5XYZZS4FE2O4L66IFBUUFZAVA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:W5XYZZS4FE2O4L66IFBUUFZAVA","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":"3175023d8f9fcbbd020755f4632a9cc2b2ae73a3f56a2f477ccecae4d074c5b2","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-01-23T13:40:55Z","title_canon_sha256":"c3c2ca1bc202fa86a9dc5d6e7f7f93fbb86409c7e0e6de388c349183796b5c0b"},"schema_version":"1.0","source":{"id":"1401.5969","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.5969","created_at":"2026-05-18T00:24:45Z"},{"alias_kind":"arxiv_version","alias_value":"1401.5969v3","created_at":"2026-05-18T00:24:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.5969","created_at":"2026-05-18T00:24:45Z"},{"alias_kind":"pith_short_12","alias_value":"W5XYZZS4FE2O","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"W5XYZZS4FE2O4L66","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"W5XYZZS4","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:53bb9f5331bd1bbfcaf46a2f2383874d5ecf42902741811861debf80609b1c7c","target":"graph","created_at":"2026-05-18T00:24:45Z","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 introduce a new family of shift spaces --- the subordinate shifts. Using subordinate shifts we prove in an elementary way that for every nonnegative real number $t$ there is a shift space with entropy $t$.","authors_text":"Dominik Kwietniak, Jian Li, Marcin Kulczycki","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-01-23T13:40:55Z","title":"Entropy of subordinate shift spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.5969","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":"sha256:5ab99ea615c4e0054ea1ad3f78dcb144c3444b77c31e9452457e1ea2a9d94fae","target":"record","created_at":"2026-05-18T00:24:45Z","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":"3175023d8f9fcbbd020755f4632a9cc2b2ae73a3f56a2f477ccecae4d074c5b2","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-01-23T13:40:55Z","title_canon_sha256":"c3c2ca1bc202fa86a9dc5d6e7f7f93fbb86409c7e0e6de388c349183796b5c0b"},"schema_version":"1.0","source":{"id":"1401.5969","kind":"arxiv","version":3}},"canonical_sha256":"b76f8ce65c2934ee2fde41434a1720a80a59bb820d426c18d489b383e941c177","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b76f8ce65c2934ee2fde41434a1720a80a59bb820d426c18d489b383e941c177","first_computed_at":"2026-05-18T00:24:45.684527Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:45.684527Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FEu4YC4KlCMcAxjaaUBwZl9VxT7QP8+fhd7kJI2QOR55Su3QRkLJNb80XQwlqtWzwA3bS2vxmfbfC+R3tslqAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:45.685019Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.5969","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ab99ea615c4e0054ea1ad3f78dcb144c3444b77c31e9452457e1ea2a9d94fae","sha256:53bb9f5331bd1bbfcaf46a2f2383874d5ecf42902741811861debf80609b1c7c"],"state_sha256":"a7714b728e1ae89624629a57d583a6ba84e9fda54090f71c0c008cab1646d6db"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vBmHLgEYjLZHODFlPmy8mfbx4VCp2BocihbYFBcg1kc36vqj+wd1tp6gI7mebuzMaHfBY+zoNvXZzdKWgwg/Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T11:43:06.331392Z","bundle_sha256":"ad618a87885056335a1f324a1b1fef4ddc2ccb7c01ff55eee9f85063563e1c63"}}