{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:66IH2NWLEIL5C2R5Y5GSSH5YMQ","short_pith_number":"pith:66IH2NWL","canonical_record":{"source":{"id":"1511.09203","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.EC","submitted_at":"2015-11-30T08:53:34Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"8265c7af9b05cce3f271cb2fabd4bb5c544c28a03b59d02a0291792012aaf43f","abstract_canon_sha256":"36c75f310f43e7cfa4c0ba6e83fa402fdc3bb663241c88b48ccbfb291aca63a8"},"schema_version":"1.0"},"canonical_sha256":"f7907d36cb2217d16a3dc74d291fb8641774ecde1e37ed34d85577edfa6f0460","source":{"kind":"arxiv","id":"1511.09203","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.09203","created_at":"2026-05-18T00:47:21Z"},{"alias_kind":"arxiv_version","alias_value":"1511.09203v4","created_at":"2026-05-18T00:47:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.09203","created_at":"2026-05-18T00:47:21Z"},{"alias_kind":"pith_short_12","alias_value":"66IH2NWLEIL5","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"66IH2NWLEIL5C2R5","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"66IH2NWL","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:66IH2NWLEIL5C2R5Y5GSSH5YMQ","target":"record","payload":{"canonical_record":{"source":{"id":"1511.09203","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.EC","submitted_at":"2015-11-30T08:53:34Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"8265c7af9b05cce3f271cb2fabd4bb5c544c28a03b59d02a0291792012aaf43f","abstract_canon_sha256":"36c75f310f43e7cfa4c0ba6e83fa402fdc3bb663241c88b48ccbfb291aca63a8"},"schema_version":"1.0"},"canonical_sha256":"f7907d36cb2217d16a3dc74d291fb8641774ecde1e37ed34d85577edfa6f0460","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:21.224107Z","signature_b64":"XjrQU9DNkKEKl2oFKDWu6nY7B/+j3itpiGeQtARAJxhA6moMe2RqMSA36dAfWqsZdAs0wLuYbrNpwSkoByIBDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f7907d36cb2217d16a3dc74d291fb8641774ecde1e37ed34d85577edfa6f0460","last_reissued_at":"2026-05-18T00:47:21.223546Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:21.223546Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.09203","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:47:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rVJb86JkhPd51IjQaGw/2Z024cPITnimuElhoWfqHRTo3Ig/UyqY29kuXm1fle5GtxLZCfZt2hppfN3kL8/FBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T14:34:10.627211Z"},"content_sha256":"f4928ad2fc36bf14135cf66da5fe0efe7859519e0456be570089246971155515","schema_version":"1.0","event_id":"sha256:f4928ad2fc36bf14135cf66da5fe0efe7859519e0456be570089246971155515"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:66IH2NWLEIL5C2R5Y5GSSH5YMQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Statistical mechanics of complex economies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"q-fin.EC","authors_text":"Giacomo Livan, Marco Bardoscia, Matteo Marsili","submitted_at":"2015-11-30T08:53:34Z","abstract_excerpt":"In the pursuit of ever increasing efficiency and growth, our economies have evolved to remarkable degrees of complexity, with nested production processes feeding each other in order to create products of greater sophistication from less sophisticated ones, down to raw materials. The engine of such an expansion have been competitive markets that, according to General Equilibrium Theory (GET), achieve efficient allocations under specific conditions. We study large random economies within the GET framework, as templates of complex economies, and we find that a non-trivial phase transition occurs:"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.09203","kind":"arxiv","version":4},"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":"2026-05-18T00:47:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"46m7zvmLAI3GaBku1oabFyWPlLzIswlS3hNHD7/Hw90JS6S8EOyf0/bmVzV3kAV68MtFumQ22T1KFx3m4+TpBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T14:34:10.627573Z"},"content_sha256":"9463e6c29ef4ac2c6331e29b2555284b7935f094e80cee1ccf34fd743fa3ad02","schema_version":"1.0","event_id":"sha256:9463e6c29ef4ac2c6331e29b2555284b7935f094e80cee1ccf34fd743fa3ad02"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/66IH2NWLEIL5C2R5Y5GSSH5YMQ/bundle.json","state_url":"https://pith.science/pith/66IH2NWLEIL5C2R5Y5GSSH5YMQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/66IH2NWLEIL5C2R5Y5GSSH5YMQ/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":"2026-05-28T14:34:10Z","links":{"resolver":"https://pith.science/pith/66IH2NWLEIL5C2R5Y5GSSH5YMQ","bundle":"https://pith.science/pith/66IH2NWLEIL5C2R5Y5GSSH5YMQ/bundle.json","state":"https://pith.science/pith/66IH2NWLEIL5C2R5Y5GSSH5YMQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/66IH2NWLEIL5C2R5Y5GSSH5YMQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:66IH2NWLEIL5C2R5Y5GSSH5YMQ","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":"36c75f310f43e7cfa4c0ba6e83fa402fdc3bb663241c88b48ccbfb291aca63a8","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.EC","submitted_at":"2015-11-30T08:53:34Z","title_canon_sha256":"8265c7af9b05cce3f271cb2fabd4bb5c544c28a03b59d02a0291792012aaf43f"},"schema_version":"1.0","source":{"id":"1511.09203","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.09203","created_at":"2026-05-18T00:47:21Z"},{"alias_kind":"arxiv_version","alias_value":"1511.09203v4","created_at":"2026-05-18T00:47:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.09203","created_at":"2026-05-18T00:47:21Z"},{"alias_kind":"pith_short_12","alias_value":"66IH2NWLEIL5","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"66IH2NWLEIL5C2R5","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"66IH2NWL","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:9463e6c29ef4ac2c6331e29b2555284b7935f094e80cee1ccf34fd743fa3ad02","target":"graph","created_at":"2026-05-18T00:47:21Z","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 the pursuit of ever increasing efficiency and growth, our economies have evolved to remarkable degrees of complexity, with nested production processes feeding each other in order to create products of greater sophistication from less sophisticated ones, down to raw materials. The engine of such an expansion have been competitive markets that, according to General Equilibrium Theory (GET), achieve efficient allocations under specific conditions. We study large random economies within the GET framework, as templates of complex economies, and we find that a non-trivial phase transition occurs:","authors_text":"Giacomo Livan, Marco Bardoscia, Matteo Marsili","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.EC","submitted_at":"2015-11-30T08:53:34Z","title":"Statistical mechanics of complex economies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.09203","kind":"arxiv","version":4},"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:f4928ad2fc36bf14135cf66da5fe0efe7859519e0456be570089246971155515","target":"record","created_at":"2026-05-18T00:47:21Z","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":"36c75f310f43e7cfa4c0ba6e83fa402fdc3bb663241c88b48ccbfb291aca63a8","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.EC","submitted_at":"2015-11-30T08:53:34Z","title_canon_sha256":"8265c7af9b05cce3f271cb2fabd4bb5c544c28a03b59d02a0291792012aaf43f"},"schema_version":"1.0","source":{"id":"1511.09203","kind":"arxiv","version":4}},"canonical_sha256":"f7907d36cb2217d16a3dc74d291fb8641774ecde1e37ed34d85577edfa6f0460","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f7907d36cb2217d16a3dc74d291fb8641774ecde1e37ed34d85577edfa6f0460","first_computed_at":"2026-05-18T00:47:21.223546Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:21.223546Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XjrQU9DNkKEKl2oFKDWu6nY7B/+j3itpiGeQtARAJxhA6moMe2RqMSA36dAfWqsZdAs0wLuYbrNpwSkoByIBDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:21.224107Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.09203","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f4928ad2fc36bf14135cf66da5fe0efe7859519e0456be570089246971155515","sha256:9463e6c29ef4ac2c6331e29b2555284b7935f094e80cee1ccf34fd743fa3ad02"],"state_sha256":"4340c80a6911cc76a70cce488961f005d0c208e03138dbb81442ffbf136d08e5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bs+UkRHQTQyodOqW2Qq4VrXWWH1Vn0VHb/2E2RJpbpIot89STcCt25Mkt2J7qOrNoPy8aSbk58aybjP+pN2jBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T14:34:10.629509Z","bundle_sha256":"b7fe331d88ae3e7eac41ee09906339e1fce564b6790135294bc7297f74b5c8ea"}}