{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:IJFKLJXJKXMKHGGVJSWEWEYNIU","short_pith_number":"pith:IJFKLJXJ","canonical_record":{"source":{"id":"1011.0637","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2010-11-02T15:18:41Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"c526b25172a013aff3d3c74b52847f01ac782d3c6036d19c477aecaf9c66a61c","abstract_canon_sha256":"d806bda746e1e570f4acff5119a9cfa42d4f289c26ea2be7c086601b7e3c8f10"},"schema_version":"1.0"},"canonical_sha256":"424aa5a6e955d8a398d54cac4b130d45123dcd3dd6957e1c80ca2c644a942686","source":{"kind":"arxiv","id":"1011.0637","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.0637","created_at":"2026-05-18T02:04:53Z"},{"alias_kind":"arxiv_version","alias_value":"1011.0637v1","created_at":"2026-05-18T02:04:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.0637","created_at":"2026-05-18T02:04:53Z"},{"alias_kind":"pith_short_12","alias_value":"IJFKLJXJKXMK","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IJFKLJXJKXMKHGGV","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IJFKLJXJ","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:IJFKLJXJKXMKHGGVJSWEWEYNIU","target":"record","payload":{"canonical_record":{"source":{"id":"1011.0637","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2010-11-02T15:18:41Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"c526b25172a013aff3d3c74b52847f01ac782d3c6036d19c477aecaf9c66a61c","abstract_canon_sha256":"d806bda746e1e570f4acff5119a9cfa42d4f289c26ea2be7c086601b7e3c8f10"},"schema_version":"1.0"},"canonical_sha256":"424aa5a6e955d8a398d54cac4b130d45123dcd3dd6957e1c80ca2c644a942686","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:04:53.644286Z","signature_b64":"l01FPMqg2J8RvyghBJFpeXZ6GR20HZRcLLgPPpBP1c67KZZoESEIL8ihK0MCGLhkHpz3+YeJEGXjUoHcI2FjBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"424aa5a6e955d8a398d54cac4b130d45123dcd3dd6957e1c80ca2c644a942686","last_reissued_at":"2026-05-18T02:04:53.643569Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:04:53.643569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.0637","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":"2026-05-18T02:04:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0G+v3+qJGss5a6+AasRNF3FFwq3UPNOTyly+jQ1oNzHQGhE6jHgPlI4IqA7MZCndWMq5Vsb+BE4z7xpOX8O2DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:36:08.528524Z"},"content_sha256":"d237768297a10881b9d0e7a0438db6a4273735986ba70936bd58bff0630a4de3","schema_version":"1.0","event_id":"sha256:d237768297a10881b9d0e7a0438db6a4273735986ba70936bd58bff0630a4de3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:IJFKLJXJKXMKHGGVJSWEWEYNIU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"First Order Phase Transition of a Long Polymer Chain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"cond-mat.soft","authors_text":"Charles Radin, David Aristoff","submitted_at":"2010-11-02T15:18:41Z","abstract_excerpt":"We consider a model consisting of a self-avoiding polygon occupying a variable density of the sites of a square lattice. A fixed energy is associated with each $90^\\circ$-bend of the polygon. We use a grand canonical ensemble, introducing parameters $\\mu$ and $\\beta$ to control average density and average (total) energy of the polygon, and show by Monte Carlo simulation that the model has a first order, nematic phase transition across a curve in the $\\beta$-$\\mu$ plane."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.0637","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":"2026-05-18T02:04:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LgGuff/heKVwwbfjTthr+HR5bRRn0/5bggb80lpT63TpU+VwAgDME1quyPDCmiFcPGT8ZeTKVniDBXxHBwuGDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:36:08.529231Z"},"content_sha256":"817e030d30e54bc9d7acd46dc95ef2dfd4964badf90419ef5babaf38bbca0e44","schema_version":"1.0","event_id":"sha256:817e030d30e54bc9d7acd46dc95ef2dfd4964badf90419ef5babaf38bbca0e44"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IJFKLJXJKXMKHGGVJSWEWEYNIU/bundle.json","state_url":"https://pith.science/pith/IJFKLJXJKXMKHGGVJSWEWEYNIU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IJFKLJXJKXMKHGGVJSWEWEYNIU/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":"2026-06-09T19:36:08Z","links":{"resolver":"https://pith.science/pith/IJFKLJXJKXMKHGGVJSWEWEYNIU","bundle":"https://pith.science/pith/IJFKLJXJKXMKHGGVJSWEWEYNIU/bundle.json","state":"https://pith.science/pith/IJFKLJXJKXMKHGGVJSWEWEYNIU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IJFKLJXJKXMKHGGVJSWEWEYNIU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:IJFKLJXJKXMKHGGVJSWEWEYNIU","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":"d806bda746e1e570f4acff5119a9cfa42d4f289c26ea2be7c086601b7e3c8f10","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2010-11-02T15:18:41Z","title_canon_sha256":"c526b25172a013aff3d3c74b52847f01ac782d3c6036d19c477aecaf9c66a61c"},"schema_version":"1.0","source":{"id":"1011.0637","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.0637","created_at":"2026-05-18T02:04:53Z"},{"alias_kind":"arxiv_version","alias_value":"1011.0637v1","created_at":"2026-05-18T02:04:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.0637","created_at":"2026-05-18T02:04:53Z"},{"alias_kind":"pith_short_12","alias_value":"IJFKLJXJKXMK","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IJFKLJXJKXMKHGGV","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IJFKLJXJ","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:817e030d30e54bc9d7acd46dc95ef2dfd4964badf90419ef5babaf38bbca0e44","target":"graph","created_at":"2026-05-18T02:04:53Z","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 consider a model consisting of a self-avoiding polygon occupying a variable density of the sites of a square lattice. A fixed energy is associated with each $90^\\circ$-bend of the polygon. We use a grand canonical ensemble, introducing parameters $\\mu$ and $\\beta$ to control average density and average (total) energy of the polygon, and show by Monte Carlo simulation that the model has a first order, nematic phase transition across a curve in the $\\beta$-$\\mu$ plane.","authors_text":"Charles Radin, David Aristoff","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2010-11-02T15:18:41Z","title":"First Order Phase Transition of a Long Polymer Chain"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.0637","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:d237768297a10881b9d0e7a0438db6a4273735986ba70936bd58bff0630a4de3","target":"record","created_at":"2026-05-18T02:04:53Z","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":"d806bda746e1e570f4acff5119a9cfa42d4f289c26ea2be7c086601b7e3c8f10","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2010-11-02T15:18:41Z","title_canon_sha256":"c526b25172a013aff3d3c74b52847f01ac782d3c6036d19c477aecaf9c66a61c"},"schema_version":"1.0","source":{"id":"1011.0637","kind":"arxiv","version":1}},"canonical_sha256":"424aa5a6e955d8a398d54cac4b130d45123dcd3dd6957e1c80ca2c644a942686","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"424aa5a6e955d8a398d54cac4b130d45123dcd3dd6957e1c80ca2c644a942686","first_computed_at":"2026-05-18T02:04:53.643569Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:04:53.643569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l01FPMqg2J8RvyghBJFpeXZ6GR20HZRcLLgPPpBP1c67KZZoESEIL8ihK0MCGLhkHpz3+YeJEGXjUoHcI2FjBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:04:53.644286Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.0637","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d237768297a10881b9d0e7a0438db6a4273735986ba70936bd58bff0630a4de3","sha256:817e030d30e54bc9d7acd46dc95ef2dfd4964badf90419ef5babaf38bbca0e44"],"state_sha256":"c228849b52c3154533328a296882e953fbd5b228c8468a419e13a160b047c126"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5m6WzmiLe6NCmDumfi+l9h5beFzKFsRqY7YUohyoVdz3MSQLHfhKGJfAybBNB312bcwGszIP/SnhrNVOx9huAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T19:36:08.533156Z","bundle_sha256":"bad831eb8d6518ccab701564a6f8bc0899ffb81813124f6cd148ab5fcf2e7d48"}}