{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:QKP7EROCVKWX2ISBDR7L3DBIQM","short_pith_number":"pith:QKP7EROC","canonical_record":{"source":{"id":"1508.04041","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-08-17T14:23:37Z","cross_cats_sorted":["cond-mat.stat-mech","math.DS","math.MP"],"title_canon_sha256":"34de4c9f9e887e8d7aaf7b88b148af49f7b246c6f5cb0d0e3a8c767518e6abb2","abstract_canon_sha256":"6d266a34e7441ea1ad7a6dcca01f3ce9dc49d1c6d7e16cd098611298dd3bf17b"},"schema_version":"1.0"},"canonical_sha256":"829ff245c2aaad7d22411c7ebd8c288337ba641fdb60917c2e097d4944a2a1f2","source":{"kind":"arxiv","id":"1508.04041","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.04041","created_at":"2026-05-18T00:52:34Z"},{"alias_kind":"arxiv_version","alias_value":"1508.04041v1","created_at":"2026-05-18T00:52:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.04041","created_at":"2026-05-18T00:52:34Z"},{"alias_kind":"pith_short_12","alias_value":"QKP7EROCVKWX","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"QKP7EROCVKWX2ISB","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"QKP7EROC","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:QKP7EROCVKWX2ISBDR7L3DBIQM","target":"record","payload":{"canonical_record":{"source":{"id":"1508.04041","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-08-17T14:23:37Z","cross_cats_sorted":["cond-mat.stat-mech","math.DS","math.MP"],"title_canon_sha256":"34de4c9f9e887e8d7aaf7b88b148af49f7b246c6f5cb0d0e3a8c767518e6abb2","abstract_canon_sha256":"6d266a34e7441ea1ad7a6dcca01f3ce9dc49d1c6d7e16cd098611298dd3bf17b"},"schema_version":"1.0"},"canonical_sha256":"829ff245c2aaad7d22411c7ebd8c288337ba641fdb60917c2e097d4944a2a1f2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:34.528214Z","signature_b64":"i6ITUinFCD1kMVYkMpgHGRKXdAlmUfjR8Hn+CYLGxxPnQHXfJ0VutcOggMnHj2gAUyGdZeJHd3lzL/dfbsxlDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"829ff245c2aaad7d22411c7ebd8c288337ba641fdb60917c2e097d4944a2a1f2","last_reissued_at":"2026-05-18T00:52:34.527822Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:34.527822Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.04041","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":"2026-05-18T00:52:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3tVwcXEqT6ethutr62f+hE6CxPRcSnwITJ7PSra07NAgWANmnRvBVhRpot3y2xIyV2fgVIxYxEjcVNsyY5RpAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T01:27:13.257849Z"},"content_sha256":"2bf29bd28f9494a3e6d4f0d814967038482cbc7e43e282444c3885322bdb8568","schema_version":"1.0","event_id":"sha256:2bf29bd28f9494a3e6d4f0d814967038482cbc7e43e282444c3885322bdb8568"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:QKP7EROCVKWX2ISBDR7L3DBIQM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Degenerated ground-states in a class of 1D Ising-like models: a characterization by symbolic dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.DS","math.MP"],"primary_cat":"math-ph","authors_text":"L. A. Corona, R. Salgado-Garcia","submitted_at":"2015-08-17T14:23:37Z","abstract_excerpt":"In this note we study a class of one-dimensional Ising chain having a highly degenerated set of ground-state configurations. The model consists of spin chain having infinite-range pair interactions with a given structure. We show that the set of ground-state configurations of such a model can be fully characterized by means of symbolic dynamics. Particularly we found that the set ground- state configurations defines what in symbolic dynamics is called sofic shift space. Finally we prove that this system has a non-vanishing residual entropy (the topological entropy of the shift space), which ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04041","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":"2026-05-18T00:52:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aoIHUrgS8fqMHNrQMvC5tMr5TMT9vyHZv5gR/ZLYkY/GU2q8rn4Q8swQNEEhLUDmQYiLmSzN9wISXXQNwDajCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T01:27:13.258620Z"},"content_sha256":"4f7e5efd6d89aa54dfc13fe5cfeb76c45776f2a57dc3e2e8d107309984f6f166","schema_version":"1.0","event_id":"sha256:4f7e5efd6d89aa54dfc13fe5cfeb76c45776f2a57dc3e2e8d107309984f6f166"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QKP7EROCVKWX2ISBDR7L3DBIQM/bundle.json","state_url":"https://pith.science/pith/QKP7EROCVKWX2ISBDR7L3DBIQM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QKP7EROCVKWX2ISBDR7L3DBIQM/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":"2026-06-12T01:27:13Z","links":{"resolver":"https://pith.science/pith/QKP7EROCVKWX2ISBDR7L3DBIQM","bundle":"https://pith.science/pith/QKP7EROCVKWX2ISBDR7L3DBIQM/bundle.json","state":"https://pith.science/pith/QKP7EROCVKWX2ISBDR7L3DBIQM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QKP7EROCVKWX2ISBDR7L3DBIQM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:QKP7EROCVKWX2ISBDR7L3DBIQM","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":"6d266a34e7441ea1ad7a6dcca01f3ce9dc49d1c6d7e16cd098611298dd3bf17b","cross_cats_sorted":["cond-mat.stat-mech","math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-08-17T14:23:37Z","title_canon_sha256":"34de4c9f9e887e8d7aaf7b88b148af49f7b246c6f5cb0d0e3a8c767518e6abb2"},"schema_version":"1.0","source":{"id":"1508.04041","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.04041","created_at":"2026-05-18T00:52:34Z"},{"alias_kind":"arxiv_version","alias_value":"1508.04041v1","created_at":"2026-05-18T00:52:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.04041","created_at":"2026-05-18T00:52:34Z"},{"alias_kind":"pith_short_12","alias_value":"QKP7EROCVKWX","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"QKP7EROCVKWX2ISB","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"QKP7EROC","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:4f7e5efd6d89aa54dfc13fe5cfeb76c45776f2a57dc3e2e8d107309984f6f166","target":"graph","created_at":"2026-05-18T00:52:34Z","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":"In this note we study a class of one-dimensional Ising chain having a highly degenerated set of ground-state configurations. The model consists of spin chain having infinite-range pair interactions with a given structure. We show that the set of ground-state configurations of such a model can be fully characterized by means of symbolic dynamics. Particularly we found that the set ground- state configurations defines what in symbolic dynamics is called sofic shift space. Finally we prove that this system has a non-vanishing residual entropy (the topological entropy of the shift space), which ca","authors_text":"L. A. Corona, R. Salgado-Garcia","cross_cats":["cond-mat.stat-mech","math.DS","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-08-17T14:23:37Z","title":"Degenerated ground-states in a class of 1D Ising-like models: a characterization by symbolic dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04041","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":"sha256:2bf29bd28f9494a3e6d4f0d814967038482cbc7e43e282444c3885322bdb8568","target":"record","created_at":"2026-05-18T00:52:34Z","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":"6d266a34e7441ea1ad7a6dcca01f3ce9dc49d1c6d7e16cd098611298dd3bf17b","cross_cats_sorted":["cond-mat.stat-mech","math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-08-17T14:23:37Z","title_canon_sha256":"34de4c9f9e887e8d7aaf7b88b148af49f7b246c6f5cb0d0e3a8c767518e6abb2"},"schema_version":"1.0","source":{"id":"1508.04041","kind":"arxiv","version":1}},"canonical_sha256":"829ff245c2aaad7d22411c7ebd8c288337ba641fdb60917c2e097d4944a2a1f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"829ff245c2aaad7d22411c7ebd8c288337ba641fdb60917c2e097d4944a2a1f2","first_computed_at":"2026-05-18T00:52:34.527822Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:34.527822Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i6ITUinFCD1kMVYkMpgHGRKXdAlmUfjR8Hn+CYLGxxPnQHXfJ0VutcOggMnHj2gAUyGdZeJHd3lzL/dfbsxlDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:34.528214Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.04041","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2bf29bd28f9494a3e6d4f0d814967038482cbc7e43e282444c3885322bdb8568","sha256:4f7e5efd6d89aa54dfc13fe5cfeb76c45776f2a57dc3e2e8d107309984f6f166"],"state_sha256":"392f4bd19a96920b7121a1f60749ccc83ae87df6b3853a5a39d2cf4a78b5e233"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3vDKzwgifLse8HIl/grGCkBentjzWsbp84o2Jt5QHGLwsnt0pPeAk1bW6BKrx50oSiG381/VDmx4vej1dNPwBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T01:27:13.262998Z","bundle_sha256":"36435a197c431ed66ff7d9b80292bbbc664becf8574faaf6f1c92e88fba10b77"}}