{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:7AL5X3FAODEQXOYTGNPD553U5G","short_pith_number":"pith:7AL5X3FA","canonical_record":{"source":{"id":"1105.6021","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cond-mat.str-el","submitted_at":"2011-05-30T15:50:35Z","cross_cats_sorted":[],"title_canon_sha256":"3ff1280dc7ad8a97dc0137527f115ecf2da7831207ddc36dd3e86b9632672034","abstract_canon_sha256":"8007f0285d0849c745cc78114017227a6b12112ac481d54b70756c808915a99a"},"schema_version":"1.0"},"canonical_sha256":"f817dbeca070c90bbb13335e3ef774e9a209747828fab7c310d36869135fb19c","source":{"kind":"arxiv","id":"1105.6021","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.6021","created_at":"2026-05-18T04:01:26Z"},{"alias_kind":"arxiv_version","alias_value":"1105.6021v2","created_at":"2026-05-18T04:01:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.6021","created_at":"2026-05-18T04:01:26Z"},{"alias_kind":"pith_short_12","alias_value":"7AL5X3FAODEQ","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7AL5X3FAODEQXOYT","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7AL5X3FA","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:7AL5X3FAODEQXOYTGNPD553U5G","target":"record","payload":{"canonical_record":{"source":{"id":"1105.6021","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cond-mat.str-el","submitted_at":"2011-05-30T15:50:35Z","cross_cats_sorted":[],"title_canon_sha256":"3ff1280dc7ad8a97dc0137527f115ecf2da7831207ddc36dd3e86b9632672034","abstract_canon_sha256":"8007f0285d0849c745cc78114017227a6b12112ac481d54b70756c808915a99a"},"schema_version":"1.0"},"canonical_sha256":"f817dbeca070c90bbb13335e3ef774e9a209747828fab7c310d36869135fb19c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:01:26.256889Z","signature_b64":"kTphO6GmxlE4m2OiHLFZn2jWy/l0jsUwRowzL/IQ4SwGaEpsCecujd+6PXZpd8Es2QUHEaKdDELtHGbTn2loCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f817dbeca070c90bbb13335e3ef774e9a209747828fab7c310d36869135fb19c","last_reissued_at":"2026-05-18T04:01:26.256341Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:01:26.256341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.6021","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":"2026-05-18T04:01:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"svcQ3kUojUKurnRNCVKlqM1MmabOVG9k8d0QTcJWcid5Gv0p8NxS6CZXEK6cUBcZlaMCbm5FRampl4GWaD4sAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T15:42:39.178347Z"},"content_sha256":"09508060c929fa391b5e4dcf7597401a79c058e2a29c5c226874b49b82a40ca5","schema_version":"1.0","event_id":"sha256:09508060c929fa391b5e4dcf7597401a79c058e2a29c5c226874b49b82a40ca5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:7AL5X3FAODEQXOYTGNPD553U5G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Symmetry protected topological orders of 1D spin systems with D2+T symmetry","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.str-el","authors_text":"Xiao-Gang Wen, Xie Chen, Zheng-Xin Liu","submitted_at":"2011-05-30T15:50:35Z","abstract_excerpt":"In [Z.-X. Liu, M. Liu, X.-G. Wen, arXiv:1101.5680], we studied 8 gapped symmetric quantum phases in S=1 spin chains %/ladders which respect a discrete spin rotation $D_2 \\subset SO(3)$ and time reversal $T$ symmetries. In this paper, using a generalized approach, we study all the 16 possible gapped symmetric quantum phases of 1D integer spin systems with only $D_2+T$ symmetry. Those phases are beyond Landau symmetry breaking theory and cannot be characterized by local order parameters, since they do not break any symmetry. They correspond to 16 symmetry protected topological (SPT) orders. We s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.6021","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":"2026-05-18T04:01:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wWa+ZnJdG/CrrvN7TSgn4vxpT/THbp1IOPY4IObzlQ4tNDhrr6zOmliatUYhhrJ36I9t728QJqdNlo6Yzp6TBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T15:42:39.178936Z"},"content_sha256":"b619d38deb82db806fbcd50ca7ecff10be138af7f58f3b8da07787e07cd7f305","schema_version":"1.0","event_id":"sha256:b619d38deb82db806fbcd50ca7ecff10be138af7f58f3b8da07787e07cd7f305"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7AL5X3FAODEQXOYTGNPD553U5G/bundle.json","state_url":"https://pith.science/pith/7AL5X3FAODEQXOYTGNPD553U5G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7AL5X3FAODEQXOYTGNPD553U5G/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":"2026-05-26T15:42:39Z","links":{"resolver":"https://pith.science/pith/7AL5X3FAODEQXOYTGNPD553U5G","bundle":"https://pith.science/pith/7AL5X3FAODEQXOYTGNPD553U5G/bundle.json","state":"https://pith.science/pith/7AL5X3FAODEQXOYTGNPD553U5G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7AL5X3FAODEQXOYTGNPD553U5G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7AL5X3FAODEQXOYTGNPD553U5G","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":"8007f0285d0849c745cc78114017227a6b12112ac481d54b70756c808915a99a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cond-mat.str-el","submitted_at":"2011-05-30T15:50:35Z","title_canon_sha256":"3ff1280dc7ad8a97dc0137527f115ecf2da7831207ddc36dd3e86b9632672034"},"schema_version":"1.0","source":{"id":"1105.6021","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.6021","created_at":"2026-05-18T04:01:26Z"},{"alias_kind":"arxiv_version","alias_value":"1105.6021v2","created_at":"2026-05-18T04:01:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.6021","created_at":"2026-05-18T04:01:26Z"},{"alias_kind":"pith_short_12","alias_value":"7AL5X3FAODEQ","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7AL5X3FAODEQXOYT","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7AL5X3FA","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:b619d38deb82db806fbcd50ca7ecff10be138af7f58f3b8da07787e07cd7f305","target":"graph","created_at":"2026-05-18T04:01:26Z","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 [Z.-X. Liu, M. Liu, X.-G. Wen, arXiv:1101.5680], we studied 8 gapped symmetric quantum phases in S=1 spin chains %/ladders which respect a discrete spin rotation $D_2 \\subset SO(3)$ and time reversal $T$ symmetries. In this paper, using a generalized approach, we study all the 16 possible gapped symmetric quantum phases of 1D integer spin systems with only $D_2+T$ symmetry. Those phases are beyond Landau symmetry breaking theory and cannot be characterized by local order parameters, since they do not break any symmetry. They correspond to 16 symmetry protected topological (SPT) orders. We s","authors_text":"Xiao-Gang Wen, Xie Chen, Zheng-Xin Liu","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cond-mat.str-el","submitted_at":"2011-05-30T15:50:35Z","title":"Symmetry protected topological orders of 1D spin systems with D2+T symmetry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.6021","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":"sha256:09508060c929fa391b5e4dcf7597401a79c058e2a29c5c226874b49b82a40ca5","target":"record","created_at":"2026-05-18T04:01:26Z","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":"8007f0285d0849c745cc78114017227a6b12112ac481d54b70756c808915a99a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cond-mat.str-el","submitted_at":"2011-05-30T15:50:35Z","title_canon_sha256":"3ff1280dc7ad8a97dc0137527f115ecf2da7831207ddc36dd3e86b9632672034"},"schema_version":"1.0","source":{"id":"1105.6021","kind":"arxiv","version":2}},"canonical_sha256":"f817dbeca070c90bbb13335e3ef774e9a209747828fab7c310d36869135fb19c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f817dbeca070c90bbb13335e3ef774e9a209747828fab7c310d36869135fb19c","first_computed_at":"2026-05-18T04:01:26.256341Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:01:26.256341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kTphO6GmxlE4m2OiHLFZn2jWy/l0jsUwRowzL/IQ4SwGaEpsCecujd+6PXZpd8Es2QUHEaKdDELtHGbTn2loCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:01:26.256889Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.6021","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:09508060c929fa391b5e4dcf7597401a79c058e2a29c5c226874b49b82a40ca5","sha256:b619d38deb82db806fbcd50ca7ecff10be138af7f58f3b8da07787e07cd7f305"],"state_sha256":"0a8fb6676bec377e7a074c7928139568095316d2c18c949626e82fc641c64b25"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QIi2QPpjm8xnPNy/Bj70GjeMwbjyzqFW6cfY4c4ZLVvmGRUs9htQl+LgviY6JGZ4KS1Sbta5VE1v0j+wk2xjDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T15:42:39.181439Z","bundle_sha256":"0ac5a2000256f201a5d8ac0bc21033aee8478de5782e62d8b2e0a5987ef09ce4"}}