{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:4T4ZZ3IKULDV3Y2KD5LHQOFF2R","short_pith_number":"pith:4T4ZZ3IK","canonical_record":{"source":{"id":"0712.4209","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cs.IT","submitted_at":"2007-12-27T10:11:02Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"468aa73df1fc8043502b90f5ece74089e43d38ecd448e75addc937a2fc4f20c9","abstract_canon_sha256":"b9c72efc6a1d75edd19a8d2f42e18aba34f910465e644c65c2e5932292e4655b"},"schema_version":"1.0"},"canonical_sha256":"e4f99ced0aa2c75de34a1f567838a5d448ddc32c6c1f1bed3341130ab3b4764d","source":{"kind":"arxiv","id":"0712.4209","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0712.4209","created_at":"2026-05-18T00:59:11Z"},{"alias_kind":"arxiv_version","alias_value":"0712.4209v1","created_at":"2026-05-18T00:59:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.4209","created_at":"2026-05-18T00:59:11Z"},{"alias_kind":"pith_short_12","alias_value":"4T4ZZ3IKULDV","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"4T4ZZ3IKULDV3Y2K","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"4T4ZZ3IK","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:4T4ZZ3IKULDV3Y2KD5LHQOFF2R","target":"record","payload":{"canonical_record":{"source":{"id":"0712.4209","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cs.IT","submitted_at":"2007-12-27T10:11:02Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"468aa73df1fc8043502b90f5ece74089e43d38ecd448e75addc937a2fc4f20c9","abstract_canon_sha256":"b9c72efc6a1d75edd19a8d2f42e18aba34f910465e644c65c2e5932292e4655b"},"schema_version":"1.0"},"canonical_sha256":"e4f99ced0aa2c75de34a1f567838a5d448ddc32c6c1f1bed3341130ab3b4764d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:11.961764Z","signature_b64":"J5damHIJQXrfAITzEyf0CS4L1DVN+D7g6g9jY/iqAYgeHTfnCki03MeBdpdFXIITAUicCoiSKEUo/IOrsJYmDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4f99ced0aa2c75de34a1f567838a5d448ddc32c6c1f1bed3341130ab3b4764d","last_reissued_at":"2026-05-18T00:59:11.961216Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:11.961216Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0712.4209","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":"2026-05-18T00:59:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MtcRlc35J58b9M24DmRr2cmXJqY5JrAcIERmNmUNdvB6UfOzQt4wExuerRbOEDMOd/zJpE/NgaIBYcMkIbhpDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:34:47.503741Z"},"content_sha256":"21662cfa3da80eb6709ee210afb38503abfeca3ab9d8e0d0e4c4f5fbb00c3587","schema_version":"1.0","event_id":"sha256:21662cfa3da80eb6709ee210afb38503abfeca3ab9d8e0d0e4c4f5fbb00c3587"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:4T4ZZ3IKULDV3Y2KD5LHQOFF2R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Generalized Random Energy Model and its Application to the Statistical Physics of Ensembles of Hierarchical Codes","license":"","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Neri Merhav","submitted_at":"2007-12-27T10:11:02Z","abstract_excerpt":"In an earlier work, the statistical physics associated with finite--temperature decoding of code ensembles, along with the relation to their random coding error exponents, were explored in a framework that is analogous to Derrida's random energy model (REM) of spin glasses, according to which the energy levels of the various spin configurations are independent random variables. The generalized REM (GREM) extends the REM in that it introduces correlations between energy levels in an hierarchical structure. In this paper, we explore some analogies between the behavior of the GREM and that of cod"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.4209","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":"2026-05-18T00:59:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0MOe/Ke20P7aAZgq3JWDfpvl3pp+lko3UluMS0lw3WwnCH/0YavAWLaLW4qESyRFlsAmI4tOnazHy95vjSpOCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:34:47.504091Z"},"content_sha256":"ec0906d6ff6d9a241072c370ec4c594d93840121b7560bcedfd786c6964d1764","schema_version":"1.0","event_id":"sha256:ec0906d6ff6d9a241072c370ec4c594d93840121b7560bcedfd786c6964d1764"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4T4ZZ3IKULDV3Y2KD5LHQOFF2R/bundle.json","state_url":"https://pith.science/pith/4T4ZZ3IKULDV3Y2KD5LHQOFF2R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4T4ZZ3IKULDV3Y2KD5LHQOFF2R/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":"2026-05-28T10:34:47Z","links":{"resolver":"https://pith.science/pith/4T4ZZ3IKULDV3Y2KD5LHQOFF2R","bundle":"https://pith.science/pith/4T4ZZ3IKULDV3Y2KD5LHQOFF2R/bundle.json","state":"https://pith.science/pith/4T4ZZ3IKULDV3Y2KD5LHQOFF2R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4T4ZZ3IKULDV3Y2KD5LHQOFF2R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:4T4ZZ3IKULDV3Y2KD5LHQOFF2R","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":"b9c72efc6a1d75edd19a8d2f42e18aba34f910465e644c65c2e5932292e4655b","cross_cats_sorted":["math.IT"],"license":"","primary_cat":"cs.IT","submitted_at":"2007-12-27T10:11:02Z","title_canon_sha256":"468aa73df1fc8043502b90f5ece74089e43d38ecd448e75addc937a2fc4f20c9"},"schema_version":"1.0","source":{"id":"0712.4209","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0712.4209","created_at":"2026-05-18T00:59:11Z"},{"alias_kind":"arxiv_version","alias_value":"0712.4209v1","created_at":"2026-05-18T00:59:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.4209","created_at":"2026-05-18T00:59:11Z"},{"alias_kind":"pith_short_12","alias_value":"4T4ZZ3IKULDV","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"4T4ZZ3IKULDV3Y2K","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"4T4ZZ3IK","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:ec0906d6ff6d9a241072c370ec4c594d93840121b7560bcedfd786c6964d1764","target":"graph","created_at":"2026-05-18T00:59:11Z","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":"In an earlier work, the statistical physics associated with finite--temperature decoding of code ensembles, along with the relation to their random coding error exponents, were explored in a framework that is analogous to Derrida's random energy model (REM) of spin glasses, according to which the energy levels of the various spin configurations are independent random variables. The generalized REM (GREM) extends the REM in that it introduces correlations between energy levels in an hierarchical structure. In this paper, we explore some analogies between the behavior of the GREM and that of cod","authors_text":"Neri Merhav","cross_cats":["math.IT"],"headline":"","license":"","primary_cat":"cs.IT","submitted_at":"2007-12-27T10:11:02Z","title":"The Generalized Random Energy Model and its Application to the Statistical Physics of Ensembles of Hierarchical Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.4209","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":"sha256:21662cfa3da80eb6709ee210afb38503abfeca3ab9d8e0d0e4c4f5fbb00c3587","target":"record","created_at":"2026-05-18T00:59:11Z","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":"b9c72efc6a1d75edd19a8d2f42e18aba34f910465e644c65c2e5932292e4655b","cross_cats_sorted":["math.IT"],"license":"","primary_cat":"cs.IT","submitted_at":"2007-12-27T10:11:02Z","title_canon_sha256":"468aa73df1fc8043502b90f5ece74089e43d38ecd448e75addc937a2fc4f20c9"},"schema_version":"1.0","source":{"id":"0712.4209","kind":"arxiv","version":1}},"canonical_sha256":"e4f99ced0aa2c75de34a1f567838a5d448ddc32c6c1f1bed3341130ab3b4764d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4f99ced0aa2c75de34a1f567838a5d448ddc32c6c1f1bed3341130ab3b4764d","first_computed_at":"2026-05-18T00:59:11.961216Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:11.961216Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J5damHIJQXrfAITzEyf0CS4L1DVN+D7g6g9jY/iqAYgeHTfnCki03MeBdpdFXIITAUicCoiSKEUo/IOrsJYmDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:11.961764Z","signed_message":"canonical_sha256_bytes"},"source_id":"0712.4209","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21662cfa3da80eb6709ee210afb38503abfeca3ab9d8e0d0e4c4f5fbb00c3587","sha256:ec0906d6ff6d9a241072c370ec4c594d93840121b7560bcedfd786c6964d1764"],"state_sha256":"fc51ac3a8c3c7dc3c4f5c9526cd16cad55efbb0f677925ef4e33ee997c9df091"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hYS8pUX1Rt2t0pn/soY8ZWP2NBnDzQfiOtX+SY590/CjveM1EWYjdcFG3bsvfgiCiRJVAC1phUGJkBliDpF0Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T10:34:47.506042Z","bundle_sha256":"5f0fcde09c75ced956bae6ce4add35f91696ad7255ba9f4efd8a8d46c80e10ad"}}