{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:LCR7N57TE7Q7AUV3OLSZUURVXV","short_pith_number":"pith:LCR7N57T","canonical_record":{"source":{"id":"2403.19068","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2024-03-28T00:17:26Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"df6a119032c5522472538756c61655d8c8eb1c587170925fa88d40c9b819c542","abstract_canon_sha256":"6936544ccb56419cc29a03afc7fe078025e63f4050cc17da3a3df02f943097f2"},"schema_version":"1.0"},"canonical_sha256":"58a3f6f7f327e1f052bb72e59a5235bd671bcd9593566c95fab595ec406aaafa","source":{"kind":"arxiv","id":"2403.19068","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.19068","created_at":"2026-07-05T10:21:18Z"},{"alias_kind":"arxiv_version","alias_value":"2403.19068v1","created_at":"2026-07-05T10:21:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.19068","created_at":"2026-07-05T10:21:18Z"},{"alias_kind":"pith_short_12","alias_value":"LCR7N57TE7Q7","created_at":"2026-07-05T10:21:18Z"},{"alias_kind":"pith_short_16","alias_value":"LCR7N57TE7Q7AUV3","created_at":"2026-07-05T10:21:18Z"},{"alias_kind":"pith_short_8","alias_value":"LCR7N57T","created_at":"2026-07-05T10:21:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:LCR7N57TE7Q7AUV3OLSZUURVXV","target":"record","payload":{"canonical_record":{"source":{"id":"2403.19068","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2024-03-28T00:17:26Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"df6a119032c5522472538756c61655d8c8eb1c587170925fa88d40c9b819c542","abstract_canon_sha256":"6936544ccb56419cc29a03afc7fe078025e63f4050cc17da3a3df02f943097f2"},"schema_version":"1.0"},"canonical_sha256":"58a3f6f7f327e1f052bb72e59a5235bd671bcd9593566c95fab595ec406aaafa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:21:18.497208Z","signature_b64":"3S5zEHTUALAHndlIZ1yB34YO+4b3IGVigGcJVrSTw2It7bQLic4wf8Pld9/ci790GcT7nyHgANpl/1CcYtbIBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58a3f6f7f327e1f052bb72e59a5235bd671bcd9593566c95fab595ec406aaafa","last_reissued_at":"2026-07-05T10:21:18.496702Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:21:18.496702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2403.19068","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":"2026-07-05T10:21:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xQy0z2IwaCX/u09xLqs1qqPg2aUGMeY0h0YjQNB1gGs8eSBL0BCbs99e2g8ToRsAGKTvsBngnm71xVllXuw+AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T12:35:45.666952Z"},"content_sha256":"d724dd7c04c8511909079886772f94ddff5c5d4a7dffd990b1056528c4f67f8a","schema_version":"1.0","event_id":"sha256:d724dd7c04c8511909079886772f94ddff5c5d4a7dffd990b1056528c4f67f8a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:LCR7N57TE7Q7AUV3OLSZUURVXV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fusion of one-dimensional gapped phases and their domain walls","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"cond-mat.str-el","authors_text":"David T. Stephen, Xie Chen","submitted_at":"2024-03-28T00:17:26Z","abstract_excerpt":"Finite depth quantum circuits provide an equivalence relation between gapped phases. Moreover, there can be nontrivial domain walls either within the same gapped phase or between different gapped phases, whose equivalence relations are given by finite depth quantum circuits in one lower dimension. In this paper, we use such unitary equivalence relations to study the fusion of one-dimensional gapped phases. In particular, we use finite depth circuits to fuse two gapped phases, local unitaries to fuse two domain walls, and a combination of both to fuse gapped phases with domain walls. This provi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.19068","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2403.19068/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T10:21:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mfju2iaz9g5TU143Qyhmwd1xh9gGszXAdGtcecJqvmRhm1syWpd7cGdzJPULYMe2JzFxNBOsh2fMDOsk3DFRCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T12:35:45.668634Z"},"content_sha256":"03f1b6769131d4cf6dbc0e69a40c77980eb6a72d75a993d34e71e97def63ed03","schema_version":"1.0","event_id":"sha256:03f1b6769131d4cf6dbc0e69a40c77980eb6a72d75a993d34e71e97def63ed03"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LCR7N57TE7Q7AUV3OLSZUURVXV/bundle.json","state_url":"https://pith.science/pith/LCR7N57TE7Q7AUV3OLSZUURVXV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LCR7N57TE7Q7AUV3OLSZUURVXV/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":"2026-08-18T12:35:45Z","links":{"resolver":"https://pith.science/pith/LCR7N57TE7Q7AUV3OLSZUURVXV","bundle":"https://pith.science/pith/LCR7N57TE7Q7AUV3OLSZUURVXV/bundle.json","state":"https://pith.science/pith/LCR7N57TE7Q7AUV3OLSZUURVXV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LCR7N57TE7Q7AUV3OLSZUURVXV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:LCR7N57TE7Q7AUV3OLSZUURVXV","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":"6936544ccb56419cc29a03afc7fe078025e63f4050cc17da3a3df02f943097f2","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2024-03-28T00:17:26Z","title_canon_sha256":"df6a119032c5522472538756c61655d8c8eb1c587170925fa88d40c9b819c542"},"schema_version":"1.0","source":{"id":"2403.19068","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.19068","created_at":"2026-07-05T10:21:18Z"},{"alias_kind":"arxiv_version","alias_value":"2403.19068v1","created_at":"2026-07-05T10:21:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.19068","created_at":"2026-07-05T10:21:18Z"},{"alias_kind":"pith_short_12","alias_value":"LCR7N57TE7Q7","created_at":"2026-07-05T10:21:18Z"},{"alias_kind":"pith_short_16","alias_value":"LCR7N57TE7Q7AUV3","created_at":"2026-07-05T10:21:18Z"},{"alias_kind":"pith_short_8","alias_value":"LCR7N57T","created_at":"2026-07-05T10:21:18Z"}],"graph_snapshots":[{"event_id":"sha256:03f1b6769131d4cf6dbc0e69a40c77980eb6a72d75a993d34e71e97def63ed03","target":"graph","created_at":"2026-07-05T10:21:18Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2403.19068/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Finite depth quantum circuits provide an equivalence relation between gapped phases. Moreover, there can be nontrivial domain walls either within the same gapped phase or between different gapped phases, whose equivalence relations are given by finite depth quantum circuits in one lower dimension. In this paper, we use such unitary equivalence relations to study the fusion of one-dimensional gapped phases. In particular, we use finite depth circuits to fuse two gapped phases, local unitaries to fuse two domain walls, and a combination of both to fuse gapped phases with domain walls. This provi","authors_text":"David T. Stephen, Xie Chen","cross_cats":["quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2024-03-28T00:17:26Z","title":"Fusion of one-dimensional gapped phases and their domain walls"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.19068","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:d724dd7c04c8511909079886772f94ddff5c5d4a7dffd990b1056528c4f67f8a","target":"record","created_at":"2026-07-05T10:21:18Z","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":"6936544ccb56419cc29a03afc7fe078025e63f4050cc17da3a3df02f943097f2","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2024-03-28T00:17:26Z","title_canon_sha256":"df6a119032c5522472538756c61655d8c8eb1c587170925fa88d40c9b819c542"},"schema_version":"1.0","source":{"id":"2403.19068","kind":"arxiv","version":1}},"canonical_sha256":"58a3f6f7f327e1f052bb72e59a5235bd671bcd9593566c95fab595ec406aaafa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"58a3f6f7f327e1f052bb72e59a5235bd671bcd9593566c95fab595ec406aaafa","first_computed_at":"2026-07-05T10:21:18.496702Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:21:18.496702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3S5zEHTUALAHndlIZ1yB34YO+4b3IGVigGcJVrSTw2It7bQLic4wf8Pld9/ci790GcT7nyHgANpl/1CcYtbIBw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:21:18.497208Z","signed_message":"canonical_sha256_bytes"},"source_id":"2403.19068","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d724dd7c04c8511909079886772f94ddff5c5d4a7dffd990b1056528c4f67f8a","sha256:03f1b6769131d4cf6dbc0e69a40c77980eb6a72d75a993d34e71e97def63ed03"],"state_sha256":"cecddca97c28f3d2f27a115f1e3d2129abf6d61993ef78739f66a39fc79931b1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rg4u82D/FLJvCOcCDO7Cq5x2CfV8+/9gGSNV6hZbAqa8YyyIwyxgu5CRhC2RkNyT9+5cXxN0XNm+1fAprGR9Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T12:35:45.677628Z","bundle_sha256":"facae4e0d8697c1bc47287d2d83fbc111b4c738ade341656c48a5c1bf3a02d65"}}