{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:I34NA7UVUSRI4ELOJHBRB6EH7B","short_pith_number":"pith:I34NA7UV","canonical_record":{"source":{"id":"1709.05105","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-09-15T08:43:52Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"0a458b9896b4deceae2b0e813aaef90a5bfcd9f7bee34fdcb716e000ce3d274d","abstract_canon_sha256":"15d0a149cd1a4a860043f396c6604b8c9e687a25cb5b64f3f3bfa5bd199c18e4"},"schema_version":"1.0"},"canonical_sha256":"46f8d07e95a4a28e116e49c310f887f87a09e859a0b3085b849eac5cbb3faebb","source":{"kind":"arxiv","id":"1709.05105","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.05105","created_at":"2026-05-18T00:35:03Z"},{"alias_kind":"arxiv_version","alias_value":"1709.05105v1","created_at":"2026-05-18T00:35:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.05105","created_at":"2026-05-18T00:35:03Z"},{"alias_kind":"pith_short_12","alias_value":"I34NA7UVUSRI","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"I34NA7UVUSRI4ELO","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"I34NA7UV","created_at":"2026-05-18T12:31:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:I34NA7UVUSRI4ELOJHBRB6EH7B","target":"record","payload":{"canonical_record":{"source":{"id":"1709.05105","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-09-15T08:43:52Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"0a458b9896b4deceae2b0e813aaef90a5bfcd9f7bee34fdcb716e000ce3d274d","abstract_canon_sha256":"15d0a149cd1a4a860043f396c6604b8c9e687a25cb5b64f3f3bfa5bd199c18e4"},"schema_version":"1.0"},"canonical_sha256":"46f8d07e95a4a28e116e49c310f887f87a09e859a0b3085b849eac5cbb3faebb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:03.283847Z","signature_b64":"UNh/+dmsQfuiO49WPGW9dE4UgYgjZtVEh46J8dSfH50uQFv0b+vRjbKftYq390MpWquBte4FoGWHTY3VaAuZCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46f8d07e95a4a28e116e49c310f887f87a09e859a0b3085b849eac5cbb3faebb","last_reissued_at":"2026-05-18T00:35:03.283229Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:03.283229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.05105","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":"2026-05-18T00:35:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UygiDbadYLGIwpQ12XjhdDgmuQ4yERGH4kXQ2LPBmfsMIN2ssfzC3gfRiXckM6KOwCr/7fmFLQKE6jtNLmg5Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T21:46:19.114848Z"},"content_sha256":"93b2b59918a242be0555441372f1cc037ebb048cc3651f264569429dadf4b140","schema_version":"1.0","event_id":"sha256:93b2b59918a242be0555441372f1cc037ebb048cc3651f264569429dadf4b140"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:I34NA7UVUSRI4ELOJHBRB6EH7B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Independence and Capacity of Multidimensional Semiconstrained Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.DS","authors_text":"Moshe Schwartz, Ohad Elishco, Tom Meyerovitch","submitted_at":"2017-09-15T08:43:52Z","abstract_excerpt":"We find a new formula for the limit of the capacity of certain sequences of multidimensional semiconstrained systems as the dimension tends to infinity. We do so by generalizing the notion of independence entropy, originally studied in the context of constrained systems, to the study of semiconstrained systems. Using the independence entropy, we obtain new lower bounds on the capacity of multidimensional semiconstrained systems in general, and $d$-dimensional axial-product systems in particular. In the case of the latter, we prove our bound is asymptotically tight, giving the exact limiting ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.05105","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":"2026-05-18T00:35:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zcW0LxNryOFYvWnSGrufxmqHl1aeyqvxRY7TF6uPKp7JlckeNBszC5KEBzjssRkJ6zz7MoXjR52yPxeLw+UfDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T21:46:19.115546Z"},"content_sha256":"1a060f2630673e85441a7a37e52b9e2ea70081ac7fb15b62cdcc1be39c5522af","schema_version":"1.0","event_id":"sha256:1a060f2630673e85441a7a37e52b9e2ea70081ac7fb15b62cdcc1be39c5522af"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I34NA7UVUSRI4ELOJHBRB6EH7B/bundle.json","state_url":"https://pith.science/pith/I34NA7UVUSRI4ELOJHBRB6EH7B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I34NA7UVUSRI4ELOJHBRB6EH7B/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":"2026-06-11T21:46:19Z","links":{"resolver":"https://pith.science/pith/I34NA7UVUSRI4ELOJHBRB6EH7B","bundle":"https://pith.science/pith/I34NA7UVUSRI4ELOJHBRB6EH7B/bundle.json","state":"https://pith.science/pith/I34NA7UVUSRI4ELOJHBRB6EH7B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I34NA7UVUSRI4ELOJHBRB6EH7B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:I34NA7UVUSRI4ELOJHBRB6EH7B","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":"15d0a149cd1a4a860043f396c6604b8c9e687a25cb5b64f3f3bfa5bd199c18e4","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-09-15T08:43:52Z","title_canon_sha256":"0a458b9896b4deceae2b0e813aaef90a5bfcd9f7bee34fdcb716e000ce3d274d"},"schema_version":"1.0","source":{"id":"1709.05105","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.05105","created_at":"2026-05-18T00:35:03Z"},{"alias_kind":"arxiv_version","alias_value":"1709.05105v1","created_at":"2026-05-18T00:35:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.05105","created_at":"2026-05-18T00:35:03Z"},{"alias_kind":"pith_short_12","alias_value":"I34NA7UVUSRI","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"I34NA7UVUSRI4ELO","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"I34NA7UV","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:1a060f2630673e85441a7a37e52b9e2ea70081ac7fb15b62cdcc1be39c5522af","target":"graph","created_at":"2026-05-18T00:35:03Z","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 find a new formula for the limit of the capacity of certain sequences of multidimensional semiconstrained systems as the dimension tends to infinity. We do so by generalizing the notion of independence entropy, originally studied in the context of constrained systems, to the study of semiconstrained systems. Using the independence entropy, we obtain new lower bounds on the capacity of multidimensional semiconstrained systems in general, and $d$-dimensional axial-product systems in particular. In the case of the latter, we prove our bound is asymptotically tight, giving the exact limiting ca","authors_text":"Moshe Schwartz, Ohad Elishco, Tom Meyerovitch","cross_cats":["cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-09-15T08:43:52Z","title":"On Independence and Capacity of Multidimensional Semiconstrained Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.05105","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":"sha256:93b2b59918a242be0555441372f1cc037ebb048cc3651f264569429dadf4b140","target":"record","created_at":"2026-05-18T00:35:03Z","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":"15d0a149cd1a4a860043f396c6604b8c9e687a25cb5b64f3f3bfa5bd199c18e4","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-09-15T08:43:52Z","title_canon_sha256":"0a458b9896b4deceae2b0e813aaef90a5bfcd9f7bee34fdcb716e000ce3d274d"},"schema_version":"1.0","source":{"id":"1709.05105","kind":"arxiv","version":1}},"canonical_sha256":"46f8d07e95a4a28e116e49c310f887f87a09e859a0b3085b849eac5cbb3faebb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46f8d07e95a4a28e116e49c310f887f87a09e859a0b3085b849eac5cbb3faebb","first_computed_at":"2026-05-18T00:35:03.283229Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:03.283229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UNh/+dmsQfuiO49WPGW9dE4UgYgjZtVEh46J8dSfH50uQFv0b+vRjbKftYq390MpWquBte4FoGWHTY3VaAuZCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:03.283847Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.05105","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:93b2b59918a242be0555441372f1cc037ebb048cc3651f264569429dadf4b140","sha256:1a060f2630673e85441a7a37e52b9e2ea70081ac7fb15b62cdcc1be39c5522af"],"state_sha256":"583a9cd461cf2d604dc1d2f1c4f0e221819b5b559bf8290099ae000cfbabd54f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bov6EQTiMYWNL00yFPyINaY1i/VH7hpd5mtn4GqKktqQOwHsg0UCBSed9QhcVwa0YIK+oEa08GgNMYDOfK5tBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T21:46:19.119816Z","bundle_sha256":"61926459f5068752ddbad007dea4acf6321a708804e029e30ac79a9dfe4b7ac1"}}