{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:ELTIUDD2ECUB3O3ODW34P52ZYD","short_pith_number":"pith:ELTIUDD2","schema_version":"1.0","canonical_sha256":"22e68a0c7a20a81dbb6e1db7c7f759c0f6de1484460996b028dd15322f1e37f3","source":{"kind":"arxiv","id":"1208.0421","version":2},"attestation_state":"computed","paper":{"title":"Exact theory of dense amorphous hard spheres in high dimension. I. The free energy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn"],"primary_cat":"cond-mat.stat-mech","authors_text":"Francesco Zamponi, Giorgio Parisi, Jorge Kurchan","submitted_at":"2012-08-02T07:25:05Z","abstract_excerpt":"We consider the theory of the glass transition and jamming of hard spheres in the large space dimension limit. Previous investigations were based on the assumption that the probability distribution within a \"cage\" is Gaussian, which is not fully consistent with numerical results. Here we perform a replica calculation without making any assumption on the cage shape. We show that thermodynamic functions turn out to be exact within the Gaussian ansatz -- provided one allows for arbitrary replica symmetry breaking --- and indeed agree well with numerical results. The actual structure function (the"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1208.0421","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-08-02T07:25:05Z","cross_cats_sorted":["cond-mat.dis-nn"],"title_canon_sha256":"34880b247b6c6f1a43502840ea6038236311cce628e631d888b0f4db0e8c715d","abstract_canon_sha256":"2a78cacc0db50e538476cbfd821ac11068f4065abf3205d7e136da515fd93885"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:04.898642Z","signature_b64":"tUZdF2B/cMYkGlsurI01cyCG/ruHsM7Eam91u1h3I1yUGxmJbcSQNNuz6MeW0OzYY+imU+LlQEvj+ydQ3fEtBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22e68a0c7a20a81dbb6e1db7c7f759c0f6de1484460996b028dd15322f1e37f3","last_reissued_at":"2026-05-18T03:43:04.898023Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:04.898023Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exact theory of dense amorphous hard spheres in high dimension. I. The free energy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn"],"primary_cat":"cond-mat.stat-mech","authors_text":"Francesco Zamponi, Giorgio Parisi, Jorge Kurchan","submitted_at":"2012-08-02T07:25:05Z","abstract_excerpt":"We consider the theory of the glass transition and jamming of hard spheres in the large space dimension limit. Previous investigations were based on the assumption that the probability distribution within a \"cage\" is Gaussian, which is not fully consistent with numerical results. Here we perform a replica calculation without making any assumption on the cage shape. We show that thermodynamic functions turn out to be exact within the Gaussian ansatz -- provided one allows for arbitrary replica symmetry breaking --- and indeed agree well with numerical results. The actual structure function (the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.0421","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1208.0421","created_at":"2026-05-18T03:43:04.898116+00:00"},{"alias_kind":"arxiv_version","alias_value":"1208.0421v2","created_at":"2026-05-18T03:43:04.898116+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.0421","created_at":"2026-05-18T03:43:04.898116+00:00"},{"alias_kind":"pith_short_12","alias_value":"ELTIUDD2ECUB","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_16","alias_value":"ELTIUDD2ECUB3O3O","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_8","alias_value":"ELTIUDD2","created_at":"2026-05-18T12:27:04.183437+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ELTIUDD2ECUB3O3ODW34P52ZYD","json":"https://pith.science/pith/ELTIUDD2ECUB3O3ODW34P52ZYD.json","graph_json":"https://pith.science/api/pith-number/ELTIUDD2ECUB3O3ODW34P52ZYD/graph.json","events_json":"https://pith.science/api/pith-number/ELTIUDD2ECUB3O3ODW34P52ZYD/events.json","paper":"https://pith.science/paper/ELTIUDD2"},"agent_actions":{"view_html":"https://pith.science/pith/ELTIUDD2ECUB3O3ODW34P52ZYD","download_json":"https://pith.science/pith/ELTIUDD2ECUB3O3ODW34P52ZYD.json","view_paper":"https://pith.science/paper/ELTIUDD2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1208.0421&json=true","fetch_graph":"https://pith.science/api/pith-number/ELTIUDD2ECUB3O3ODW34P52ZYD/graph.json","fetch_events":"https://pith.science/api/pith-number/ELTIUDD2ECUB3O3ODW34P52ZYD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ELTIUDD2ECUB3O3ODW34P52ZYD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ELTIUDD2ECUB3O3ODW34P52ZYD/action/storage_attestation","attest_author":"https://pith.science/pith/ELTIUDD2ECUB3O3ODW34P52ZYD/action/author_attestation","sign_citation":"https://pith.science/pith/ELTIUDD2ECUB3O3ODW34P52ZYD/action/citation_signature","submit_replication":"https://pith.science/pith/ELTIUDD2ECUB3O3ODW34P52ZYD/action/replication_record"}},"created_at":"2026-05-18T03:43:04.898116+00:00","updated_at":"2026-05-18T03:43:04.898116+00:00"}