{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:NTGFM4FS7W5DNLMU7I6SH57Q5Y","short_pith_number":"pith:NTGFM4FS","schema_version":"1.0","canonical_sha256":"6ccc5670b2fdba36ad94fa3d23f7f0ee105c605340fbd86e451ab223e15e92a2","source":{"kind":"arxiv","id":"1507.03036","version":2},"attestation_state":"computed","paper":{"title":"String Bits at Finite Temperature and the Hagedorn Phase","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Charles B. Thorn","submitted_at":"2015-07-10T21:42:43Z","abstract_excerpt":"We study the behavior of a simple string bit model at finite temperature. We use thermal perturbation theory to analyze the high temperature regime. But at low temperatures we rely on the large $N$ limit of the dynamics, for which the exact energy spectrum is known. Since the lowest energy states at infinite $N$ are free closed strings, the $N=\\infty$ partition function diverges above a finite temperature $\\beta_H^{-1}$, the Hagedorn temperature. We argue that in these models at finite $N$, which then have a finite number of degrees of freedom, there can be neither an ultimate temperature nor "},"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":"1507.03036","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-07-10T21:42:43Z","cross_cats_sorted":[],"title_canon_sha256":"63ebad3ae61a0f49266601119255bdd0e71720dec90a5c2e5525775574fa795a","abstract_canon_sha256":"aef23cd8c0d9a4d3defbc2c97dcdd6c305f8d7a8cc6b52820d314ca5e502626c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:11.811832Z","signature_b64":"IKM9svC9AKULF1Y+4CTQ5FA9ywQNKyAsRgIWOvr7aQIAO/MraFnFLO/tXgS1+yB3I55Xy82QCh88paKP62CNDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ccc5670b2fdba36ad94fa3d23f7f0ee105c605340fbd86e451ab223e15e92a2","last_reissued_at":"2026-05-18T00:38:11.811089Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:11.811089Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"String Bits at Finite Temperature and the Hagedorn Phase","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Charles B. Thorn","submitted_at":"2015-07-10T21:42:43Z","abstract_excerpt":"We study the behavior of a simple string bit model at finite temperature. We use thermal perturbation theory to analyze the high temperature regime. But at low temperatures we rely on the large $N$ limit of the dynamics, for which the exact energy spectrum is known. Since the lowest energy states at infinite $N$ are free closed strings, the $N=\\infty$ partition function diverges above a finite temperature $\\beta_H^{-1}$, the Hagedorn temperature. We argue that in these models at finite $N$, which then have a finite number of degrees of freedom, there can be neither an ultimate temperature nor "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03036","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":"1507.03036","created_at":"2026-05-18T00:38:11.811225+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.03036v2","created_at":"2026-05-18T00:38:11.811225+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.03036","created_at":"2026-05-18T00:38:11.811225+00:00"},{"alias_kind":"pith_short_12","alias_value":"NTGFM4FS7W5D","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_16","alias_value":"NTGFM4FS7W5DNLMU","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_8","alias_value":"NTGFM4FS","created_at":"2026-05-18T12:29:34.919912+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/NTGFM4FS7W5DNLMU7I6SH57Q5Y","json":"https://pith.science/pith/NTGFM4FS7W5DNLMU7I6SH57Q5Y.json","graph_json":"https://pith.science/api/pith-number/NTGFM4FS7W5DNLMU7I6SH57Q5Y/graph.json","events_json":"https://pith.science/api/pith-number/NTGFM4FS7W5DNLMU7I6SH57Q5Y/events.json","paper":"https://pith.science/paper/NTGFM4FS"},"agent_actions":{"view_html":"https://pith.science/pith/NTGFM4FS7W5DNLMU7I6SH57Q5Y","download_json":"https://pith.science/pith/NTGFM4FS7W5DNLMU7I6SH57Q5Y.json","view_paper":"https://pith.science/paper/NTGFM4FS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.03036&json=true","fetch_graph":"https://pith.science/api/pith-number/NTGFM4FS7W5DNLMU7I6SH57Q5Y/graph.json","fetch_events":"https://pith.science/api/pith-number/NTGFM4FS7W5DNLMU7I6SH57Q5Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NTGFM4FS7W5DNLMU7I6SH57Q5Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NTGFM4FS7W5DNLMU7I6SH57Q5Y/action/storage_attestation","attest_author":"https://pith.science/pith/NTGFM4FS7W5DNLMU7I6SH57Q5Y/action/author_attestation","sign_citation":"https://pith.science/pith/NTGFM4FS7W5DNLMU7I6SH57Q5Y/action/citation_signature","submit_replication":"https://pith.science/pith/NTGFM4FS7W5DNLMU7I6SH57Q5Y/action/replication_record"}},"created_at":"2026-05-18T00:38:11.811225+00:00","updated_at":"2026-05-18T00:38:11.811225+00:00"}