{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:SLKLJUIIGMWDOC6ZHBYX54K2D2","short_pith_number":"pith:SLKLJUII","canonical_record":{"source":{"id":"1412.0006","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-11-27T18:08:10Z","cross_cats_sorted":[],"title_canon_sha256":"8b330aa81b6cea23fe1e68b4f0daf967df8084d6809ab9c17177750f00b67fd1","abstract_canon_sha256":"045bc036e4854d7f182afa4184d6c87a3109ea7717a6f48e0a8a07515ed7713f"},"schema_version":"1.0"},"canonical_sha256":"92d4b4d108332c370bd938717ef15a1ea0a10c95eda751c07e22a1728c8ca166","source":{"kind":"arxiv","id":"1412.0006","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.0006","created_at":"2026-05-18T02:04:08Z"},{"alias_kind":"arxiv_version","alias_value":"1412.0006v1","created_at":"2026-05-18T02:04:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.0006","created_at":"2026-05-18T02:04:08Z"},{"alias_kind":"pith_short_12","alias_value":"SLKLJUIIGMWD","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SLKLJUIIGMWDOC6Z","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SLKLJUII","created_at":"2026-05-18T12:28:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:SLKLJUIIGMWDOC6ZHBYX54K2D2","target":"record","payload":{"canonical_record":{"source":{"id":"1412.0006","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-11-27T18:08:10Z","cross_cats_sorted":[],"title_canon_sha256":"8b330aa81b6cea23fe1e68b4f0daf967df8084d6809ab9c17177750f00b67fd1","abstract_canon_sha256":"045bc036e4854d7f182afa4184d6c87a3109ea7717a6f48e0a8a07515ed7713f"},"schema_version":"1.0"},"canonical_sha256":"92d4b4d108332c370bd938717ef15a1ea0a10c95eda751c07e22a1728c8ca166","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:04:08.098545Z","signature_b64":"iBn2rhPVm7Ew90vAGZVmJzBmNRoSeSHSkwj3j92deUP6SkeFgv3l3ECDEQtnbW9EAUtDm1jhboZbLqXCdxaNBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92d4b4d108332c370bd938717ef15a1ea0a10c95eda751c07e22a1728c8ca166","last_reissued_at":"2026-05-18T02:04:08.097828Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:04:08.097828Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.0006","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":"2026-05-18T02:04:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EF7bcMpNT8F9tTFblV8K0qERdji0sJNQhn5LyWOrgZ6KMgzoJHGbYDjcZG+Ftogy4HCOHNBqOUHclcLTz9QFAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T18:58:16.258380Z"},"content_sha256":"821483481cd5339efc7b9f958c1daa8f9d3127a35f09f8c20b8bb75d01f72fb3","schema_version":"1.0","event_id":"sha256:821483481cd5339efc7b9f958c1daa8f9d3127a35f09f8c20b8bb75d01f72fb3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:SLKLJUIIGMWDOC6ZHBYX54K2D2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Emergence of $q$-statistical functions in a generalized binomial distribution with strong correlations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Constantino Tsallis, Guiomar Ruiz","submitted_at":"2014-11-27T18:08:10Z","abstract_excerpt":"We study a symmetric generalization $\\mathfrak{p}^{(N)}_k(\\eta, \\alpha)$ of the binomial distribution recently introduced by Bergeron et al, where $\\eta \\in [0,1]$ denotes the win probability, and $\\alpha$ is a positive parameter. This generalization is based on $q$-exponential generating functions ($e_{q^{gen}}^z \\equiv [1+(1-q^{gen})z]^{1/(1-q^{gen})};\\,e_{1}^z=e^z)$ where $q^{gen}=1+1/\\alpha$. The numerical calculation of the probability distribution function of the number of wins $k$, related to the number of realizations $N$, strongly approaches a discrete $q^{disc}$-Gaussian distribution"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0006","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":"2026-05-18T02:04:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W23FEokZ6swVHYGN2T3bqYQ7DhRs5IyXelZEMt6ZbwD6MGPQyB8a6+esf2sP/suGHnsMU324rW0TxE9/bnjfDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T18:58:16.258978Z"},"content_sha256":"ba1087d26256d135a4f9d57b430a8b9d4f97aba1cb45e64e3e04e04577d6392c","schema_version":"1.0","event_id":"sha256:ba1087d26256d135a4f9d57b430a8b9d4f97aba1cb45e64e3e04e04577d6392c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SLKLJUIIGMWDOC6ZHBYX54K2D2/bundle.json","state_url":"https://pith.science/pith/SLKLJUIIGMWDOC6ZHBYX54K2D2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SLKLJUIIGMWDOC6ZHBYX54K2D2/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":"2026-05-31T18:58:16Z","links":{"resolver":"https://pith.science/pith/SLKLJUIIGMWDOC6ZHBYX54K2D2","bundle":"https://pith.science/pith/SLKLJUIIGMWDOC6ZHBYX54K2D2/bundle.json","state":"https://pith.science/pith/SLKLJUIIGMWDOC6ZHBYX54K2D2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SLKLJUIIGMWDOC6ZHBYX54K2D2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:SLKLJUIIGMWDOC6ZHBYX54K2D2","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":"045bc036e4854d7f182afa4184d6c87a3109ea7717a6f48e0a8a07515ed7713f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-11-27T18:08:10Z","title_canon_sha256":"8b330aa81b6cea23fe1e68b4f0daf967df8084d6809ab9c17177750f00b67fd1"},"schema_version":"1.0","source":{"id":"1412.0006","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.0006","created_at":"2026-05-18T02:04:08Z"},{"alias_kind":"arxiv_version","alias_value":"1412.0006v1","created_at":"2026-05-18T02:04:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.0006","created_at":"2026-05-18T02:04:08Z"},{"alias_kind":"pith_short_12","alias_value":"SLKLJUIIGMWD","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SLKLJUIIGMWDOC6Z","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SLKLJUII","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:ba1087d26256d135a4f9d57b430a8b9d4f97aba1cb45e64e3e04e04577d6392c","target":"graph","created_at":"2026-05-18T02:04:08Z","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 a symmetric generalization $\\mathfrak{p}^{(N)}_k(\\eta, \\alpha)$ of the binomial distribution recently introduced by Bergeron et al, where $\\eta \\in [0,1]$ denotes the win probability, and $\\alpha$ is a positive parameter. This generalization is based on $q$-exponential generating functions ($e_{q^{gen}}^z \\equiv [1+(1-q^{gen})z]^{1/(1-q^{gen})};\\,e_{1}^z=e^z)$ where $q^{gen}=1+1/\\alpha$. The numerical calculation of the probability distribution function of the number of wins $k$, related to the number of realizations $N$, strongly approaches a discrete $q^{disc}$-Gaussian distribution","authors_text":"Constantino Tsallis, Guiomar Ruiz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-11-27T18:08:10Z","title":"Emergence of $q$-statistical functions in a generalized binomial distribution with strong correlations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0006","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":"sha256:821483481cd5339efc7b9f958c1daa8f9d3127a35f09f8c20b8bb75d01f72fb3","target":"record","created_at":"2026-05-18T02:04:08Z","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":"045bc036e4854d7f182afa4184d6c87a3109ea7717a6f48e0a8a07515ed7713f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-11-27T18:08:10Z","title_canon_sha256":"8b330aa81b6cea23fe1e68b4f0daf967df8084d6809ab9c17177750f00b67fd1"},"schema_version":"1.0","source":{"id":"1412.0006","kind":"arxiv","version":1}},"canonical_sha256":"92d4b4d108332c370bd938717ef15a1ea0a10c95eda751c07e22a1728c8ca166","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"92d4b4d108332c370bd938717ef15a1ea0a10c95eda751c07e22a1728c8ca166","first_computed_at":"2026-05-18T02:04:08.097828Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:04:08.097828Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iBn2rhPVm7Ew90vAGZVmJzBmNRoSeSHSkwj3j92deUP6SkeFgv3l3ECDEQtnbW9EAUtDm1jhboZbLqXCdxaNBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:04:08.098545Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.0006","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:821483481cd5339efc7b9f958c1daa8f9d3127a35f09f8c20b8bb75d01f72fb3","sha256:ba1087d26256d135a4f9d57b430a8b9d4f97aba1cb45e64e3e04e04577d6392c"],"state_sha256":"ff6df080db4ed7f1370d7210d881c8f628f55ad73b581263ba93c98a0702dcf8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EZpHvtY99DLIpB2cikJvS4QgO2oMVU3DuuanOYQ+yihm7f2yvvnwiJ0kds8Hu9KAAt1SOedadxUl6PxX9EwTAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T18:58:16.261747Z","bundle_sha256":"03e094ca47ea0016b4a4f2f49196b8eddcfe3d60ccf1f63ceb34ece0ee8ad238"}}