{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:E5OVWPFC3TSAI3WUM3EAJVDY3L","short_pith_number":"pith:E5OVWPFC","canonical_record":{"source":{"id":"1102.4138","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-02-21T05:34:22Z","cross_cats_sorted":[],"title_canon_sha256":"d84e7f7a4da292d337202002cb717f5a87e774fbeb34e05c26455931b3afce21","abstract_canon_sha256":"05d0445d2dc39cc948a9c5cef08fabd746c36288081b36db7e9cf32ce08eaa47"},"schema_version":"1.0"},"canonical_sha256":"275d5b3ca2dce4046ed466c804d478daeb4d72afd73dc6e8d3ffad4f8a3c9437","source":{"kind":"arxiv","id":"1102.4138","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.4138","created_at":"2026-05-18T04:28:18Z"},{"alias_kind":"arxiv_version","alias_value":"1102.4138v1","created_at":"2026-05-18T04:28:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4138","created_at":"2026-05-18T04:28:18Z"},{"alias_kind":"pith_short_12","alias_value":"E5OVWPFC3TSA","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"E5OVWPFC3TSAI3WU","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"E5OVWPFC","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:E5OVWPFC3TSAI3WUM3EAJVDY3L","target":"record","payload":{"canonical_record":{"source":{"id":"1102.4138","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-02-21T05:34:22Z","cross_cats_sorted":[],"title_canon_sha256":"d84e7f7a4da292d337202002cb717f5a87e774fbeb34e05c26455931b3afce21","abstract_canon_sha256":"05d0445d2dc39cc948a9c5cef08fabd746c36288081b36db7e9cf32ce08eaa47"},"schema_version":"1.0"},"canonical_sha256":"275d5b3ca2dce4046ed466c804d478daeb4d72afd73dc6e8d3ffad4f8a3c9437","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:28:18.911549Z","signature_b64":"yo1Y1YbeeHOojoyxxDmGXZ9tehBrrfCEjcnGvCAtU3xkl0ImehXa+K3SEDuWP3/AVVzvR/gTjXHAMjv7V6X0Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"275d5b3ca2dce4046ed466c804d478daeb4d72afd73dc6e8d3ffad4f8a3c9437","last_reissued_at":"2026-05-18T04:28:18.910910Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:28:18.910910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.4138","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":"2026-05-18T04:28:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9XY05tN4rAP2U1Lo2i12IbucDEQOiiB7y4SF6mzK+YnwgtHvUFIEZSOfumLCHRW0YN0+W15jjb+ZhQ0gPr9EAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T16:45:22.882457Z"},"content_sha256":"efdc6a4f3b94ab14951b041a88fde71593bed25e72520bec1a48a9614aef4377","schema_version":"1.0","event_id":"sha256:efdc6a4f3b94ab14951b041a88fde71593bed25e72520bec1a48a9614aef4377"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:E5OVWPFC3TSAI3WUM3EAJVDY3L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bethe approximation for a system of hard rigid rods: the random locally tree-like layered lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Deepak Dhar, J\\\"urgen F. Stilck, R. Rajesh","submitted_at":"2011-02-21T05:34:22Z","abstract_excerpt":"We study the Bethe approximation for a system of long rigid rods of fixed length k, with only excluded volume interaction. For large enough k, this system undergoes an isotropic-nematic phase transition as a function of density of the rods. The Bethe lattice, which is conventionally used to derive the self-consistent equations in the Bethe approximation, is not suitable for studying the hard-rods system, as it does not allow a dense packing of rods. We define a new lattice, called the random locally tree-like layered lattice, which allows a dense packing of rods, and for which the approximatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4138","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":"2026-05-18T04:28:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/BEvDWT8BGwMHAjo+HFgcK22t8HFHnHjezYLNyHT6ipb/tAIpFVCD2uS5wKOnrqI5B7bmAmtDzAriVGB21CdDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T16:45:22.883111Z"},"content_sha256":"a2256f90f8a35b5c3944e1fade15a92041216eaf310244c4e203810adf86b497","schema_version":"1.0","event_id":"sha256:a2256f90f8a35b5c3944e1fade15a92041216eaf310244c4e203810adf86b497"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E5OVWPFC3TSAI3WUM3EAJVDY3L/bundle.json","state_url":"https://pith.science/pith/E5OVWPFC3TSAI3WUM3EAJVDY3L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E5OVWPFC3TSAI3WUM3EAJVDY3L/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":"2026-05-26T16:45:22Z","links":{"resolver":"https://pith.science/pith/E5OVWPFC3TSAI3WUM3EAJVDY3L","bundle":"https://pith.science/pith/E5OVWPFC3TSAI3WUM3EAJVDY3L/bundle.json","state":"https://pith.science/pith/E5OVWPFC3TSAI3WUM3EAJVDY3L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E5OVWPFC3TSAI3WUM3EAJVDY3L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:E5OVWPFC3TSAI3WUM3EAJVDY3L","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":"05d0445d2dc39cc948a9c5cef08fabd746c36288081b36db7e9cf32ce08eaa47","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-02-21T05:34:22Z","title_canon_sha256":"d84e7f7a4da292d337202002cb717f5a87e774fbeb34e05c26455931b3afce21"},"schema_version":"1.0","source":{"id":"1102.4138","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.4138","created_at":"2026-05-18T04:28:18Z"},{"alias_kind":"arxiv_version","alias_value":"1102.4138v1","created_at":"2026-05-18T04:28:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4138","created_at":"2026-05-18T04:28:18Z"},{"alias_kind":"pith_short_12","alias_value":"E5OVWPFC3TSA","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"E5OVWPFC3TSAI3WU","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"E5OVWPFC","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:a2256f90f8a35b5c3944e1fade15a92041216eaf310244c4e203810adf86b497","target":"graph","created_at":"2026-05-18T04:28:18Z","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 Bethe approximation for a system of long rigid rods of fixed length k, with only excluded volume interaction. For large enough k, this system undergoes an isotropic-nematic phase transition as a function of density of the rods. The Bethe lattice, which is conventionally used to derive the self-consistent equations in the Bethe approximation, is not suitable for studying the hard-rods system, as it does not allow a dense packing of rods. We define a new lattice, called the random locally tree-like layered lattice, which allows a dense packing of rods, and for which the approximatio","authors_text":"Deepak Dhar, J\\\"urgen F. Stilck, R. Rajesh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-02-21T05:34:22Z","title":"Bethe approximation for a system of hard rigid rods: the random locally tree-like layered lattice"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4138","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:efdc6a4f3b94ab14951b041a88fde71593bed25e72520bec1a48a9614aef4377","target":"record","created_at":"2026-05-18T04:28:18Z","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":"05d0445d2dc39cc948a9c5cef08fabd746c36288081b36db7e9cf32ce08eaa47","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-02-21T05:34:22Z","title_canon_sha256":"d84e7f7a4da292d337202002cb717f5a87e774fbeb34e05c26455931b3afce21"},"schema_version":"1.0","source":{"id":"1102.4138","kind":"arxiv","version":1}},"canonical_sha256":"275d5b3ca2dce4046ed466c804d478daeb4d72afd73dc6e8d3ffad4f8a3c9437","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"275d5b3ca2dce4046ed466c804d478daeb4d72afd73dc6e8d3ffad4f8a3c9437","first_computed_at":"2026-05-18T04:28:18.910910Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:28:18.910910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yo1Y1YbeeHOojoyxxDmGXZ9tehBrrfCEjcnGvCAtU3xkl0ImehXa+K3SEDuWP3/AVVzvR/gTjXHAMjv7V6X0Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:28:18.911549Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.4138","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:efdc6a4f3b94ab14951b041a88fde71593bed25e72520bec1a48a9614aef4377","sha256:a2256f90f8a35b5c3944e1fade15a92041216eaf310244c4e203810adf86b497"],"state_sha256":"5bb51b1cd98affb9a27f903607c514b32761ca699ff07dbc426e3733b0ce7430"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TIeoBp3RuMxx24GSrQymCfjDp5pHw9yZT2GZpBt1xwiV2GvgKzAv72hd3/XFjDepvN351sSjMaRApAGFnXRzCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T16:45:22.886666Z","bundle_sha256":"7d02a1ab3e2842d3cac6ad30231843587d595c27007d14db2b753c0378835ed8"}}