{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:QWBRQWCURYA3YQ56YL2EW7HQ7R","short_pith_number":"pith:QWBRQWCU","canonical_record":{"source":{"id":"1509.04507","kind":"arxiv","version":6},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2015-09-15T11:44:17Z","cross_cats_sorted":["cond-mat.str-el"],"title_canon_sha256":"b393e58581cf9ee760fd56d339c2fd821af3ee3e502b75c2cd4e9a6b9f6ec89d","abstract_canon_sha256":"df17e15dc31ca89dc558f985692431270bd816fa445f49b35900d39eca753a13"},"schema_version":"1.0"},"canonical_sha256":"85831858548e01bc43bec2f44b7cf0fc71996d7c897804f5577613047fd85e41","source":{"kind":"arxiv","id":"1509.04507","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.04507","created_at":"2026-05-18T00:24:45Z"},{"alias_kind":"arxiv_version","alias_value":"1509.04507v6","created_at":"2026-05-18T00:24:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.04507","created_at":"2026-05-18T00:24:45Z"},{"alias_kind":"pith_short_12","alias_value":"QWBRQWCURYA3","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"QWBRQWCURYA3YQ56","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"QWBRQWCU","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:QWBRQWCURYA3YQ56YL2EW7HQ7R","target":"record","payload":{"canonical_record":{"source":{"id":"1509.04507","kind":"arxiv","version":6},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2015-09-15T11:44:17Z","cross_cats_sorted":["cond-mat.str-el"],"title_canon_sha256":"b393e58581cf9ee760fd56d339c2fd821af3ee3e502b75c2cd4e9a6b9f6ec89d","abstract_canon_sha256":"df17e15dc31ca89dc558f985692431270bd816fa445f49b35900d39eca753a13"},"schema_version":"1.0"},"canonical_sha256":"85831858548e01bc43bec2f44b7cf0fc71996d7c897804f5577613047fd85e41","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:45.529204Z","signature_b64":"melv6VhRzEuZCmuEigTL4gVCIJXTobqyB3pV7hZSjKGrE8WKu4ZUHGp6JpOoFt6K+QC0bkbD1ZGC4iIY7HdiBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85831858548e01bc43bec2f44b7cf0fc71996d7c897804f5577613047fd85e41","last_reissued_at":"2026-05-18T00:24:45.528642Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:45.528642Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.04507","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:24:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CZFYq5PpmGLq9OvbDDA9ftzIE0qRtjyygdFUFM64t+NVSPb8v0D8lskaYyuTdl4RJKL64ZQiVDB+Y/FgdsIeCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T15:11:42.217298Z"},"content_sha256":"5211a46f6435e3c7ef23b7d4f8a75f5596473a8833844cb0837a6bd94aef5b7d","schema_version":"1.0","event_id":"sha256:5211a46f6435e3c7ef23b7d4f8a75f5596473a8833844cb0837a6bd94aef5b7d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:QWBRQWCURYA3YQ56YL2EW7HQ7R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bond dimension witnesses and the structure of homogeneous matrix product states","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.str-el"],"primary_cat":"quant-ph","authors_text":"Miguel Navascues, Tamas Vertesi","submitted_at":"2015-09-15T11:44:17Z","abstract_excerpt":"For the past twenty years, Matrix Product States (MPS) have been widely used in solid state physics to approximate the ground state of one-dimensional spin chains. In this paper, we study homogeneous MPS (hMPS), or MPS constructed via site-independent tensors and a boundary condition. Exploiting a connection with the theory of matrix algebras, we derive two structural properties shared by all hMPS, namely: a) there exist local operators which annihilate all hMPS of a given bond dimension; and b) there exist local operators which, when applied over any hMPS of a given bond dimension, decouple ("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.04507","kind":"arxiv","version":6},"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":"2026-05-18T00:24:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dEYuQt/OUcb4vkm4Gjua06EDaVh2+3ZpQkJgMEW6u62vGokeOVxg+yDwgTfVxkwFSdixP4vSWP+i6lKLcgnpCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T15:11:42.217671Z"},"content_sha256":"d7450b0e94fc45759475a2ecb12140a53047bfbb67eacf28dc1f7b5a876f1d7a","schema_version":"1.0","event_id":"sha256:d7450b0e94fc45759475a2ecb12140a53047bfbb67eacf28dc1f7b5a876f1d7a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QWBRQWCURYA3YQ56YL2EW7HQ7R/bundle.json","state_url":"https://pith.science/pith/QWBRQWCURYA3YQ56YL2EW7HQ7R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QWBRQWCURYA3YQ56YL2EW7HQ7R/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":"2026-06-09T15:11:42Z","links":{"resolver":"https://pith.science/pith/QWBRQWCURYA3YQ56YL2EW7HQ7R","bundle":"https://pith.science/pith/QWBRQWCURYA3YQ56YL2EW7HQ7R/bundle.json","state":"https://pith.science/pith/QWBRQWCURYA3YQ56YL2EW7HQ7R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QWBRQWCURYA3YQ56YL2EW7HQ7R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:QWBRQWCURYA3YQ56YL2EW7HQ7R","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":"df17e15dc31ca89dc558f985692431270bd816fa445f49b35900d39eca753a13","cross_cats_sorted":["cond-mat.str-el"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2015-09-15T11:44:17Z","title_canon_sha256":"b393e58581cf9ee760fd56d339c2fd821af3ee3e502b75c2cd4e9a6b9f6ec89d"},"schema_version":"1.0","source":{"id":"1509.04507","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.04507","created_at":"2026-05-18T00:24:45Z"},{"alias_kind":"arxiv_version","alias_value":"1509.04507v6","created_at":"2026-05-18T00:24:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.04507","created_at":"2026-05-18T00:24:45Z"},{"alias_kind":"pith_short_12","alias_value":"QWBRQWCURYA3","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"QWBRQWCURYA3YQ56","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"QWBRQWCU","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:d7450b0e94fc45759475a2ecb12140a53047bfbb67eacf28dc1f7b5a876f1d7a","target":"graph","created_at":"2026-05-18T00:24:45Z","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":"For the past twenty years, Matrix Product States (MPS) have been widely used in solid state physics to approximate the ground state of one-dimensional spin chains. In this paper, we study homogeneous MPS (hMPS), or MPS constructed via site-independent tensors and a boundary condition. Exploiting a connection with the theory of matrix algebras, we derive two structural properties shared by all hMPS, namely: a) there exist local operators which annihilate all hMPS of a given bond dimension; and b) there exist local operators which, when applied over any hMPS of a given bond dimension, decouple (","authors_text":"Miguel Navascues, Tamas Vertesi","cross_cats":["cond-mat.str-el"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2015-09-15T11:44:17Z","title":"Bond dimension witnesses and the structure of homogeneous matrix product states"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.04507","kind":"arxiv","version":6},"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":"sha256:5211a46f6435e3c7ef23b7d4f8a75f5596473a8833844cb0837a6bd94aef5b7d","target":"record","created_at":"2026-05-18T00:24:45Z","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":"df17e15dc31ca89dc558f985692431270bd816fa445f49b35900d39eca753a13","cross_cats_sorted":["cond-mat.str-el"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2015-09-15T11:44:17Z","title_canon_sha256":"b393e58581cf9ee760fd56d339c2fd821af3ee3e502b75c2cd4e9a6b9f6ec89d"},"schema_version":"1.0","source":{"id":"1509.04507","kind":"arxiv","version":6}},"canonical_sha256":"85831858548e01bc43bec2f44b7cf0fc71996d7c897804f5577613047fd85e41","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85831858548e01bc43bec2f44b7cf0fc71996d7c897804f5577613047fd85e41","first_computed_at":"2026-05-18T00:24:45.528642Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:45.528642Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"melv6VhRzEuZCmuEigTL4gVCIJXTobqyB3pV7hZSjKGrE8WKu4ZUHGp6JpOoFt6K+QC0bkbD1ZGC4iIY7HdiBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:45.529204Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.04507","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5211a46f6435e3c7ef23b7d4f8a75f5596473a8833844cb0837a6bd94aef5b7d","sha256:d7450b0e94fc45759475a2ecb12140a53047bfbb67eacf28dc1f7b5a876f1d7a"],"state_sha256":"606d18bd71d9be24f7cd788b99cedb67da088948b8ceda908657414cf0374e99"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OYF3BX+LwZq3ZnStoXY/UpBcE8+zunRgO8ZWe61rUr8y/glDdeLccdeofG9Enoqu581Zt97yeXZGdErAn9l2CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T15:11:42.219628Z","bundle_sha256":"c2908185cdba90dcc627317970c24f608616850597f2c472d764b1d30c4d59b5"}}