{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:Q6PON5ATHIERMCWLZB5TJENES6","short_pith_number":"pith:Q6PON5AT","canonical_record":{"source":{"id":"1109.0803","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"gr-qc","submitted_at":"2011-09-05T05:44:18Z","cross_cats_sorted":["cond-mat.stat-mech","hep-th"],"title_canon_sha256":"893ce136f3dc96072cd2b91e91d79b3bc72ec02a649b3238d9b95c43265e3084","abstract_canon_sha256":"74ada76934c97a3c835890668374b94f9a8ac0675b9f745ca7d9df5103dcaf35"},"schema_version":"1.0"},"canonical_sha256":"879ee6f4133a09160acbc87b3491a49781c62e602e7c8855c370b182b1e1f9ac","source":{"kind":"arxiv","id":"1109.0803","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.0803","created_at":"2026-05-18T04:07:07Z"},{"alias_kind":"arxiv_version","alias_value":"1109.0803v2","created_at":"2026-05-18T04:07:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.0803","created_at":"2026-05-18T04:07:07Z"},{"alias_kind":"pith_short_12","alias_value":"Q6PON5ATHIER","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"Q6PON5ATHIERMCWL","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"Q6PON5AT","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:Q6PON5ATHIERMCWLZB5TJENES6","target":"record","payload":{"canonical_record":{"source":{"id":"1109.0803","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"gr-qc","submitted_at":"2011-09-05T05:44:18Z","cross_cats_sorted":["cond-mat.stat-mech","hep-th"],"title_canon_sha256":"893ce136f3dc96072cd2b91e91d79b3bc72ec02a649b3238d9b95c43265e3084","abstract_canon_sha256":"74ada76934c97a3c835890668374b94f9a8ac0675b9f745ca7d9df5103dcaf35"},"schema_version":"1.0"},"canonical_sha256":"879ee6f4133a09160acbc87b3491a49781c62e602e7c8855c370b182b1e1f9ac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:07.685215Z","signature_b64":"eUxxCK4we1w3vfHZBBKsLf1hbhXZ/5AB4u1/a7bmmv3P4eBZs8p/YlqqJIQsCa8ZJW+MBQ0wl9FcdEmUfnFcDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"879ee6f4133a09160acbc87b3491a49781c62e602e7c8855c370b182b1e1f9ac","last_reissued_at":"2026-05-18T04:07:07.684442Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:07.684442Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.0803","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:07:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8DljR5C3hpsuY9IhJxN5fvbv61CW1QT6zXqmWWsdEdxwAFv4UDRb0pOc2pXQ5Xs6i/RAjlPL8qrKu2UP2TMYAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T23:21:21.970935Z"},"content_sha256":"383982e5a714bf79aa36cd9e46dd99f5f50e1b2ae43b3b2a6be30aa08ea3612d","schema_version":"1.0","event_id":"sha256:383982e5a714bf79aa36cd9e46dd99f5f50e1b2ae43b3b2a6be30aa08ea3612d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:Q6PON5ATHIERMCWLZB5TJENES6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Statistical Thermodynamics of Polymer Quantum Systems","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["cond-mat.stat-mech","hep-th"],"primary_cat":"gr-qc","authors_text":"Elisa Manrique, Guillermo Chac\\'on-Acosta, Hugo A. Morales-T\\'ecotl, Leonardo Dagdug","submitted_at":"2011-09-05T05:44:18Z","abstract_excerpt":"Polymer quantum systems are mechanical models quantized similarly as loop quantum gravity. It is actually in quantizing gravity that the polymer term holds proper as the quantum geometry excitations yield a reminiscent of a polymer material. In such an approach both non-singular cosmological models and a microscopic basis for the entropy of some black holes have arisen. Also important physical questions for these systems involve thermodynamics. With this motivation, in this work, we study the statistical thermodynamics of two one dimensional {\\em polymer} quantum systems: an ensemble of oscill"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0803","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:07:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vxAV1FO3NaIoKD67HKGO1f4QOtVUFo9/gCbPsYUZ1uGWvHEYrd7HdHEz4JO3gT3dxCS8NQ5sXb2kypujAHV1CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T23:21:21.971281Z"},"content_sha256":"5119ff9809787c6665311ff4e7324f7181c8d18533ef7fc4c6427835b1e255bf","schema_version":"1.0","event_id":"sha256:5119ff9809787c6665311ff4e7324f7181c8d18533ef7fc4c6427835b1e255bf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q6PON5ATHIERMCWLZB5TJENES6/bundle.json","state_url":"https://pith.science/pith/Q6PON5ATHIERMCWLZB5TJENES6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q6PON5ATHIERMCWLZB5TJENES6/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":"2026-06-30T23:21:21Z","links":{"resolver":"https://pith.science/pith/Q6PON5ATHIERMCWLZB5TJENES6","bundle":"https://pith.science/pith/Q6PON5ATHIERMCWLZB5TJENES6/bundle.json","state":"https://pith.science/pith/Q6PON5ATHIERMCWLZB5TJENES6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q6PON5ATHIERMCWLZB5TJENES6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:Q6PON5ATHIERMCWLZB5TJENES6","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":"74ada76934c97a3c835890668374b94f9a8ac0675b9f745ca7d9df5103dcaf35","cross_cats_sorted":["cond-mat.stat-mech","hep-th"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"gr-qc","submitted_at":"2011-09-05T05:44:18Z","title_canon_sha256":"893ce136f3dc96072cd2b91e91d79b3bc72ec02a649b3238d9b95c43265e3084"},"schema_version":"1.0","source":{"id":"1109.0803","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.0803","created_at":"2026-05-18T04:07:07Z"},{"alias_kind":"arxiv_version","alias_value":"1109.0803v2","created_at":"2026-05-18T04:07:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.0803","created_at":"2026-05-18T04:07:07Z"},{"alias_kind":"pith_short_12","alias_value":"Q6PON5ATHIER","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"Q6PON5ATHIERMCWL","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"Q6PON5AT","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:5119ff9809787c6665311ff4e7324f7181c8d18533ef7fc4c6427835b1e255bf","target":"graph","created_at":"2026-05-18T04:07:07Z","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":"Polymer quantum systems are mechanical models quantized similarly as loop quantum gravity. It is actually in quantizing gravity that the polymer term holds proper as the quantum geometry excitations yield a reminiscent of a polymer material. In such an approach both non-singular cosmological models and a microscopic basis for the entropy of some black holes have arisen. Also important physical questions for these systems involve thermodynamics. With this motivation, in this work, we study the statistical thermodynamics of two one dimensional {\\em polymer} quantum systems: an ensemble of oscill","authors_text":"Elisa Manrique, Guillermo Chac\\'on-Acosta, Hugo A. Morales-T\\'ecotl, Leonardo Dagdug","cross_cats":["cond-mat.stat-mech","hep-th"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"gr-qc","submitted_at":"2011-09-05T05:44:18Z","title":"Statistical Thermodynamics of Polymer Quantum Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0803","kind":"arxiv","version":2},"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":"sha256:383982e5a714bf79aa36cd9e46dd99f5f50e1b2ae43b3b2a6be30aa08ea3612d","target":"record","created_at":"2026-05-18T04:07:07Z","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":"74ada76934c97a3c835890668374b94f9a8ac0675b9f745ca7d9df5103dcaf35","cross_cats_sorted":["cond-mat.stat-mech","hep-th"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"gr-qc","submitted_at":"2011-09-05T05:44:18Z","title_canon_sha256":"893ce136f3dc96072cd2b91e91d79b3bc72ec02a649b3238d9b95c43265e3084"},"schema_version":"1.0","source":{"id":"1109.0803","kind":"arxiv","version":2}},"canonical_sha256":"879ee6f4133a09160acbc87b3491a49781c62e602e7c8855c370b182b1e1f9ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"879ee6f4133a09160acbc87b3491a49781c62e602e7c8855c370b182b1e1f9ac","first_computed_at":"2026-05-18T04:07:07.684442Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:07:07.684442Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eUxxCK4we1w3vfHZBBKsLf1hbhXZ/5AB4u1/a7bmmv3P4eBZs8p/YlqqJIQsCa8ZJW+MBQ0wl9FcdEmUfnFcDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:07:07.685215Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.0803","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:383982e5a714bf79aa36cd9e46dd99f5f50e1b2ae43b3b2a6be30aa08ea3612d","sha256:5119ff9809787c6665311ff4e7324f7181c8d18533ef7fc4c6427835b1e255bf"],"state_sha256":"21dde12dd8463fec51bafff366af2982d5a3a21fcce98ae1d30ed70a6629a89d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hXvYZi5dc5MA67gnpw9BdxsynzPp1OVrMV56JHardh+m/qZ0yormKkvhSVFkUpgMcvrU0Fb2ldinY4azoAb2Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T23:21:21.973248Z","bundle_sha256":"7bcea03a80dbbf61e6a5b076f1861ec8901b115cb9a6a8cf6f7aa672017d1b7c"}}