{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:G3IGBSY5MDNE6FZWXM4U5EN2H2","short_pith_number":"pith:G3IGBSY5","canonical_record":{"source":{"id":"cond-mat/0309655","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat","submitted_at":"2003-09-29T08:51:14Z","cross_cats_sorted":[],"title_canon_sha256":"adfe8f4feace9ca5cdaea0462fd19eb5afddcd45855c50a21f74883f14faff59","abstract_canon_sha256":"04dcc86a2c103d98fab34def69c12ea80df8c91ff011717114ea2ba934e92998"},"schema_version":"1.0"},"canonical_sha256":"36d060cb1d60da4f1736bb394e91ba3eb26d556ccd4dbb56684249acd06d1a9c","source":{"kind":"arxiv","id":"cond-mat/0309655","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0309655","created_at":"2026-05-18T01:09:02Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0309655v1","created_at":"2026-05-18T01:09:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0309655","created_at":"2026-05-18T01:09:02Z"},{"alias_kind":"pith_short_12","alias_value":"G3IGBSY5MDNE","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"G3IGBSY5MDNE6FZW","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"G3IGBSY5","created_at":"2026-05-18T12:25:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:G3IGBSY5MDNE6FZWXM4U5EN2H2","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/0309655","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat","submitted_at":"2003-09-29T08:51:14Z","cross_cats_sorted":[],"title_canon_sha256":"adfe8f4feace9ca5cdaea0462fd19eb5afddcd45855c50a21f74883f14faff59","abstract_canon_sha256":"04dcc86a2c103d98fab34def69c12ea80df8c91ff011717114ea2ba934e92998"},"schema_version":"1.0"},"canonical_sha256":"36d060cb1d60da4f1736bb394e91ba3eb26d556ccd4dbb56684249acd06d1a9c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:02.525500Z","signature_b64":"8oP8fCBZ25r5T22l2+v4iJvlaGaNwJm47NJfBYkIFYxRz8b5a13qxBgcZsJuBHG1ry1n9j3kjPFA2Kh5HFCgDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36d060cb1d60da4f1736bb394e91ba3eb26d556ccd4dbb56684249acd06d1a9c","last_reissued_at":"2026-05-18T01:09:02.525007Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:02.525007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/0309655","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":"2026-05-18T01:09:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5zM/zIOR5q3jq0112UaXB6QMVcDj4uywKTpUw6+SbXolvEHL9dJbV/uH3sYbyBncT6pnwwuqTQlsO78f9QelDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T07:44:40.679789Z"},"content_sha256":"4ce23b5abc8686623ce996c9c954a254c393e595a026e2a9793aa083929da884","schema_version":"1.0","event_id":"sha256:4ce23b5abc8686623ce996c9c954a254c393e595a026e2a9793aa083929da884"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:G3IGBSY5MDNE6FZWXM4U5EN2H2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Little-Hopfield model on a Random Graph","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat","authors_text":"I. P\\'erez Castillo, N.S. Skantzos","submitted_at":"2003-09-29T08:51:14Z","abstract_excerpt":"We study the Hopfield model on a random graph in scaling regimes where the average number of connections per neuron is a finite number and where the spin dynamics is governed by a synchronous execution of the microscopic update rule (Little-Hopfield model).We solve this model within replica symmetry and by using bifurcation analysis we prove that the spin-glass/paramagnetic and the retrieval/paramagnetictransition lines of our phase diagram are identical to those of sequential dynamics.The first-order retrieval/spin-glass transition line follows by direct evaluation of our observables using po"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0309655","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":"2026-05-18T01:09:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c+Nio4Uq3FJFxEJlrjjbCyBkd8tAhAtDVP36YCINExDQxyh0Q0MAyiBrzOr9QqzHg0hLeRBQWRjI6kSc7qHgDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T07:44:40.680141Z"},"content_sha256":"63c16b561b8b5444d70f07c990306f172059da9869f28734cca3fdf35ca0fe1e","schema_version":"1.0","event_id":"sha256:63c16b561b8b5444d70f07c990306f172059da9869f28734cca3fdf35ca0fe1e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G3IGBSY5MDNE6FZWXM4U5EN2H2/bundle.json","state_url":"https://pith.science/pith/G3IGBSY5MDNE6FZWXM4U5EN2H2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G3IGBSY5MDNE6FZWXM4U5EN2H2/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":"2026-06-03T07:44:40Z","links":{"resolver":"https://pith.science/pith/G3IGBSY5MDNE6FZWXM4U5EN2H2","bundle":"https://pith.science/pith/G3IGBSY5MDNE6FZWXM4U5EN2H2/bundle.json","state":"https://pith.science/pith/G3IGBSY5MDNE6FZWXM4U5EN2H2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G3IGBSY5MDNE6FZWXM4U5EN2H2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:G3IGBSY5MDNE6FZWXM4U5EN2H2","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":"04dcc86a2c103d98fab34def69c12ea80df8c91ff011717114ea2ba934e92998","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat","submitted_at":"2003-09-29T08:51:14Z","title_canon_sha256":"adfe8f4feace9ca5cdaea0462fd19eb5afddcd45855c50a21f74883f14faff59"},"schema_version":"1.0","source":{"id":"cond-mat/0309655","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0309655","created_at":"2026-05-18T01:09:02Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0309655v1","created_at":"2026-05-18T01:09:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0309655","created_at":"2026-05-18T01:09:02Z"},{"alias_kind":"pith_short_12","alias_value":"G3IGBSY5MDNE","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"G3IGBSY5MDNE6FZW","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"G3IGBSY5","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:63c16b561b8b5444d70f07c990306f172059da9869f28734cca3fdf35ca0fe1e","target":"graph","created_at":"2026-05-18T01:09:02Z","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 the Hopfield model on a random graph in scaling regimes where the average number of connections per neuron is a finite number and where the spin dynamics is governed by a synchronous execution of the microscopic update rule (Little-Hopfield model).We solve this model within replica symmetry and by using bifurcation analysis we prove that the spin-glass/paramagnetic and the retrieval/paramagnetictransition lines of our phase diagram are identical to those of sequential dynamics.The first-order retrieval/spin-glass transition line follows by direct evaluation of our observables using po","authors_text":"I. P\\'erez Castillo, N.S. Skantzos","cross_cats":[],"headline":"","license":"","primary_cat":"cond-mat","submitted_at":"2003-09-29T08:51:14Z","title":"The Little-Hopfield model on a Random Graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0309655","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":"sha256:4ce23b5abc8686623ce996c9c954a254c393e595a026e2a9793aa083929da884","target":"record","created_at":"2026-05-18T01:09:02Z","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":"04dcc86a2c103d98fab34def69c12ea80df8c91ff011717114ea2ba934e92998","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat","submitted_at":"2003-09-29T08:51:14Z","title_canon_sha256":"adfe8f4feace9ca5cdaea0462fd19eb5afddcd45855c50a21f74883f14faff59"},"schema_version":"1.0","source":{"id":"cond-mat/0309655","kind":"arxiv","version":1}},"canonical_sha256":"36d060cb1d60da4f1736bb394e91ba3eb26d556ccd4dbb56684249acd06d1a9c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36d060cb1d60da4f1736bb394e91ba3eb26d556ccd4dbb56684249acd06d1a9c","first_computed_at":"2026-05-18T01:09:02.525007Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:02.525007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8oP8fCBZ25r5T22l2+v4iJvlaGaNwJm47NJfBYkIFYxRz8b5a13qxBgcZsJuBHG1ry1n9j3kjPFA2Kh5HFCgDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:02.525500Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0309655","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ce23b5abc8686623ce996c9c954a254c393e595a026e2a9793aa083929da884","sha256:63c16b561b8b5444d70f07c990306f172059da9869f28734cca3fdf35ca0fe1e"],"state_sha256":"7fc307600cc29d17e37f7466ecb116c9afff9363369a925ed65b5bb1c013bd25"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3mCm/sDM8UeeGmAWYav5Jr7M4BXuC3rBReU2+NW81khmqZz0ZISB5QI8OfD5Hw2WvH9W9ZYPN0+5u+0iCA8OBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T07:44:40.682105Z","bundle_sha256":"fbc2a61c48051be1f5b2613b5bfca570c412a2c5bb1b26dbc6f9cf61035026b9"}}