{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:EIRZGHM3XMVQQ3JMA5LRIBKPAB","short_pith_number":"pith:EIRZGHM3","canonical_record":{"source":{"id":"1612.05940","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-12-18T16:23:20Z","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"title_canon_sha256":"c9ca1ba1d95432c6bf65c92e5ec4e9ce8f76bb54df2793ede8850e0e7820f9c5","abstract_canon_sha256":"9444f5bf27ae467a24d1fe10c505119f7c6e82ba3294e609f45d5db2c4a7565d"},"schema_version":"1.0"},"canonical_sha256":"2223931d9bbb2b086d2c075714054f004d898f213782ac5ba94b66d99eea7121","source":{"kind":"arxiv","id":"1612.05940","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.05940","created_at":"2026-05-18T00:26:01Z"},{"alias_kind":"arxiv_version","alias_value":"1612.05940v1","created_at":"2026-05-18T00:26:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.05940","created_at":"2026-05-18T00:26:01Z"},{"alias_kind":"pith_short_12","alias_value":"EIRZGHM3XMVQ","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"EIRZGHM3XMVQQ3JM","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"EIRZGHM3","created_at":"2026-05-18T12:30:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:EIRZGHM3XMVQQ3JMA5LRIBKPAB","target":"record","payload":{"canonical_record":{"source":{"id":"1612.05940","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-12-18T16:23:20Z","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"title_canon_sha256":"c9ca1ba1d95432c6bf65c92e5ec4e9ce8f76bb54df2793ede8850e0e7820f9c5","abstract_canon_sha256":"9444f5bf27ae467a24d1fe10c505119f7c6e82ba3294e609f45d5db2c4a7565d"},"schema_version":"1.0"},"canonical_sha256":"2223931d9bbb2b086d2c075714054f004d898f213782ac5ba94b66d99eea7121","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:01.561045Z","signature_b64":"ysxqKIXdvibHgpE2uugSwsnVF61k3VG0D5Yq9Rf72KqFmbBz/nbsTP478EviV2/GZdYsuVbL28nJyfEij9nWBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2223931d9bbb2b086d2c075714054f004d898f213782ac5ba94b66d99eea7121","last_reissued_at":"2026-05-18T00:26:01.560323Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:01.560323Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.05940","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":"2026-05-18T00:26:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EOnikJPToSsyqGKrQ8kKxQRHIZ6cY2L7CiXtBaTYoXZl4osMoa6hsAOGi4dwZ8fC5zWCx2LHV/Y9gpBAn6UMCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:06:46.141145Z"},"content_sha256":"39861ea364bffbfea4bc25088e6a4d7605f37086d775dcf2974a6772f15359b5","schema_version":"1.0","event_id":"sha256:39861ea364bffbfea4bc25088e6a4d7605f37086d775dcf2974a6772f15359b5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:EIRZGHM3XMVQQ3JMA5LRIBKPAB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Periodic and Weakly Periodic Ground States for the $\\lambda$-Model on Cayley Tree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.MP"],"primary_cat":"math-ph","authors_text":"Chin Hee Pah, Farrukh Mukhamedov, Hakim Jamil, Muzaffar Rahmatullaev","submitted_at":"2016-12-18T16:23:20Z","abstract_excerpt":"In this paper we consider the $\\lambda$-model on the Cayley tree of order two. We describe periodic and weakly periodic ground states for the considered model."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.05940","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":"2026-05-18T00:26:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+9dA2LdJ2efkRXy0BvdRC7OBd/PkCW0HsK/CX1B7Uwg2SjqICUFMGnsUaj6a8o5ZQcEpAH/IolCEUvQzK7RoBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:06:46.141502Z"},"content_sha256":"aad3e77e4fa3e2a47229e96b1f45705fd457c8e5c9622d7c39625c7b7d4ef4a3","schema_version":"1.0","event_id":"sha256:aad3e77e4fa3e2a47229e96b1f45705fd457c8e5c9622d7c39625c7b7d4ef4a3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EIRZGHM3XMVQQ3JMA5LRIBKPAB/bundle.json","state_url":"https://pith.science/pith/EIRZGHM3XMVQQ3JMA5LRIBKPAB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EIRZGHM3XMVQQ3JMA5LRIBKPAB/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":"2026-06-01T12:06:46Z","links":{"resolver":"https://pith.science/pith/EIRZGHM3XMVQQ3JMA5LRIBKPAB","bundle":"https://pith.science/pith/EIRZGHM3XMVQQ3JMA5LRIBKPAB/bundle.json","state":"https://pith.science/pith/EIRZGHM3XMVQQ3JMA5LRIBKPAB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EIRZGHM3XMVQQ3JMA5LRIBKPAB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:EIRZGHM3XMVQQ3JMA5LRIBKPAB","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":"9444f5bf27ae467a24d1fe10c505119f7c6e82ba3294e609f45d5db2c4a7565d","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-12-18T16:23:20Z","title_canon_sha256":"c9ca1ba1d95432c6bf65c92e5ec4e9ce8f76bb54df2793ede8850e0e7820f9c5"},"schema_version":"1.0","source":{"id":"1612.05940","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.05940","created_at":"2026-05-18T00:26:01Z"},{"alias_kind":"arxiv_version","alias_value":"1612.05940v1","created_at":"2026-05-18T00:26:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.05940","created_at":"2026-05-18T00:26:01Z"},{"alias_kind":"pith_short_12","alias_value":"EIRZGHM3XMVQ","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"EIRZGHM3XMVQQ3JM","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"EIRZGHM3","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:aad3e77e4fa3e2a47229e96b1f45705fd457c8e5c9622d7c39625c7b7d4ef4a3","target":"graph","created_at":"2026-05-18T00:26:01Z","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 paper we consider the $\\lambda$-model on the Cayley tree of order two. We describe periodic and weakly periodic ground states for the considered model.","authors_text":"Chin Hee Pah, Farrukh Mukhamedov, Hakim Jamil, Muzaffar Rahmatullaev","cross_cats":["cond-mat.stat-mech","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-12-18T16:23:20Z","title":"Periodic and Weakly Periodic Ground States for the $\\lambda$-Model on Cayley Tree"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.05940","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":"sha256:39861ea364bffbfea4bc25088e6a4d7605f37086d775dcf2974a6772f15359b5","target":"record","created_at":"2026-05-18T00:26:01Z","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":"9444f5bf27ae467a24d1fe10c505119f7c6e82ba3294e609f45d5db2c4a7565d","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-12-18T16:23:20Z","title_canon_sha256":"c9ca1ba1d95432c6bf65c92e5ec4e9ce8f76bb54df2793ede8850e0e7820f9c5"},"schema_version":"1.0","source":{"id":"1612.05940","kind":"arxiv","version":1}},"canonical_sha256":"2223931d9bbb2b086d2c075714054f004d898f213782ac5ba94b66d99eea7121","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2223931d9bbb2b086d2c075714054f004d898f213782ac5ba94b66d99eea7121","first_computed_at":"2026-05-18T00:26:01.560323Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:01.560323Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ysxqKIXdvibHgpE2uugSwsnVF61k3VG0D5Yq9Rf72KqFmbBz/nbsTP478EviV2/GZdYsuVbL28nJyfEij9nWBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:01.561045Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.05940","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:39861ea364bffbfea4bc25088e6a4d7605f37086d775dcf2974a6772f15359b5","sha256:aad3e77e4fa3e2a47229e96b1f45705fd457c8e5c9622d7c39625c7b7d4ef4a3"],"state_sha256":"cebf11a3afb07d9eb1167ab82e87d70ecc6d8d5c6c1752e830aea7ff86f37dfb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2wWC9vbUWT/h9FhKrHdjTV63MnAIyrgcL28OuNmn1lXCogelldcyXUvHl5w/rZ8TqRkAQOokJ7OnnqUhy8xTAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T12:06:46.143359Z","bundle_sha256":"d702b8b16c31eaba3423f264941f89448d7bfc262db114e5ac2bebd68967fbfa"}}