{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:OGN5MTV5XSHXLASJBDUGY7WM7V","short_pith_number":"pith:OGN5MTV5","canonical_record":{"source":{"id":"2608.11602","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-08-12T03:21:27Z","cross_cats_sorted":["math-ph","math.DS","math.MP"],"title_canon_sha256":"7f171def590df046996654ae286be96c54090892c3f017f238202a1fe453fada","abstract_canon_sha256":"94265c9976c3c6734b25cdce45f0d5dc579dbb0d52617433c6e49921083048c5"},"schema_version":"1.0"},"canonical_sha256":"719bd64ebdbc8f75824908e86c7eccfd7b571ba18cb418274d3c185dfc2e790c","source":{"kind":"arxiv","id":"2608.11602","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.11602","created_at":"2026-08-13T00:22:17Z"},{"alias_kind":"arxiv_version","alias_value":"2608.11602v1","created_at":"2026-08-13T00:22:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.11602","created_at":"2026-08-13T00:22:17Z"},{"alias_kind":"pith_short_12","alias_value":"OGN5MTV5XSHX","created_at":"2026-08-13T00:22:17Z"},{"alias_kind":"pith_short_16","alias_value":"OGN5MTV5XSHXLASJ","created_at":"2026-08-13T00:22:17Z"},{"alias_kind":"pith_short_8","alias_value":"OGN5MTV5","created_at":"2026-08-13T00:22:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:OGN5MTV5XSHXLASJBDUGY7WM7V","target":"record","payload":{"canonical_record":{"source":{"id":"2608.11602","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-08-12T03:21:27Z","cross_cats_sorted":["math-ph","math.DS","math.MP"],"title_canon_sha256":"7f171def590df046996654ae286be96c54090892c3f017f238202a1fe453fada","abstract_canon_sha256":"94265c9976c3c6734b25cdce45f0d5dc579dbb0d52617433c6e49921083048c5"},"schema_version":"1.0"},"canonical_sha256":"719bd64ebdbc8f75824908e86c7eccfd7b571ba18cb418274d3c185dfc2e790c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-13T00:22:17.321193Z","signature_b64":"vVHmw1fk+G2Z9HJswUVKQk1ipt/9mDyvoE2pERV9mwWj+k+iQnPTFOPw+kA0BBW85p2v9v+xKDC+l9vrKQ9fCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"719bd64ebdbc8f75824908e86c7eccfd7b571ba18cb418274d3c185dfc2e790c","last_reissued_at":"2026-08-13T00:22:17.319246Z","signature_status":"signed_v1","first_computed_at":"2026-08-13T00:22:17.319246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.11602","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":"2026-08-13T00:22:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TYC5uKPF2blOEvW6Tt8NUGQPbuyeingqiANQWIPWkqFi8yK52EkS03R+eVeyS1eg8g0J1p+HFRvuxG1Ddn7SDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T10:16:37.896137Z"},"content_sha256":"fca6a9f112061e981978bdc66f1dedb5c951a6aa4e59eafc6c72b822950aebdc","schema_version":"1.0","event_id":"sha256:fca6a9f112061e981978bdc66f1dedb5c951a6aa4e59eafc6c72b822950aebdc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:OGN5MTV5XSHXLASJBDUGY7WM7V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantitative Unique Continuation on Simplex and $\\mathbb{Z}^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DS","math.MP"],"primary_cat":"math.AP","authors_text":"Shihe Liu, Yunfeng Shi, Zhifei Zhang","submitted_at":"2026-08-12T03:21:27Z","abstract_excerpt":"In this work, we establish the quantitative unique continuation on both $n$-dimensional simplex lattice $\\Delta^{(n)}_{N}$ and $\\mathbb{Z}^n$ for arbitrary $n\\geq 3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.11602","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/2608.11602/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":"2026-08-13T00:22:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"szfljq+VlSfQg8Clhs9cXhK8rYwm3ujrzf3J8E+SETrj233/G575oaIi8nmdiJ0s1WnuD1Jk45bDN6Ij17IIAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T10:16:37.898579Z"},"content_sha256":"3b27b4cca8b9efff4f66fd2b1d5a442b9124f60d222925e46d2027c7bba77476","schema_version":"1.0","event_id":"sha256:3b27b4cca8b9efff4f66fd2b1d5a442b9124f60d222925e46d2027c7bba77476"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OGN5MTV5XSHXLASJBDUGY7WM7V/bundle.json","state_url":"https://pith.science/pith/OGN5MTV5XSHXLASJBDUGY7WM7V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OGN5MTV5XSHXLASJBDUGY7WM7V/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":"2026-08-17T10:16:37Z","links":{"resolver":"https://pith.science/pith/OGN5MTV5XSHXLASJBDUGY7WM7V","bundle":"https://pith.science/pith/OGN5MTV5XSHXLASJBDUGY7WM7V/bundle.json","state":"https://pith.science/pith/OGN5MTV5XSHXLASJBDUGY7WM7V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OGN5MTV5XSHXLASJBDUGY7WM7V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:OGN5MTV5XSHXLASJBDUGY7WM7V","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":"94265c9976c3c6734b25cdce45f0d5dc579dbb0d52617433c6e49921083048c5","cross_cats_sorted":["math-ph","math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-08-12T03:21:27Z","title_canon_sha256":"7f171def590df046996654ae286be96c54090892c3f017f238202a1fe453fada"},"schema_version":"1.0","source":{"id":"2608.11602","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.11602","created_at":"2026-08-13T00:22:17Z"},{"alias_kind":"arxiv_version","alias_value":"2608.11602v1","created_at":"2026-08-13T00:22:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.11602","created_at":"2026-08-13T00:22:17Z"},{"alias_kind":"pith_short_12","alias_value":"OGN5MTV5XSHX","created_at":"2026-08-13T00:22:17Z"},{"alias_kind":"pith_short_16","alias_value":"OGN5MTV5XSHXLASJ","created_at":"2026-08-13T00:22:17Z"},{"alias_kind":"pith_short_8","alias_value":"OGN5MTV5","created_at":"2026-08-13T00:22:17Z"}],"graph_snapshots":[{"event_id":"sha256:3b27b4cca8b9efff4f66fd2b1d5a442b9124f60d222925e46d2027c7bba77476","target":"graph","created_at":"2026-08-13T00:22:17Z","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/2608.11602/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work, we establish the quantitative unique continuation on both $n$-dimensional simplex lattice $\\Delta^{(n)}_{N}$ and $\\mathbb{Z}^n$ for arbitrary $n\\geq 3$.","authors_text":"Shihe Liu, Yunfeng Shi, Zhifei Zhang","cross_cats":["math-ph","math.DS","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-08-12T03:21:27Z","title":"Quantitative Unique Continuation on Simplex and $\\mathbb{Z}^n$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.11602","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:fca6a9f112061e981978bdc66f1dedb5c951a6aa4e59eafc6c72b822950aebdc","target":"record","created_at":"2026-08-13T00:22:17Z","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":"94265c9976c3c6734b25cdce45f0d5dc579dbb0d52617433c6e49921083048c5","cross_cats_sorted":["math-ph","math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-08-12T03:21:27Z","title_canon_sha256":"7f171def590df046996654ae286be96c54090892c3f017f238202a1fe453fada"},"schema_version":"1.0","source":{"id":"2608.11602","kind":"arxiv","version":1}},"canonical_sha256":"719bd64ebdbc8f75824908e86c7eccfd7b571ba18cb418274d3c185dfc2e790c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"719bd64ebdbc8f75824908e86c7eccfd7b571ba18cb418274d3c185dfc2e790c","first_computed_at":"2026-08-13T00:22:17.319246Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-13T00:22:17.319246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vVHmw1fk+G2Z9HJswUVKQk1ipt/9mDyvoE2pERV9mwWj+k+iQnPTFOPw+kA0BBW85p2v9v+xKDC+l9vrKQ9fCg==","signature_status":"signed_v1","signed_at":"2026-08-13T00:22:17.321193Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.11602","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fca6a9f112061e981978bdc66f1dedb5c951a6aa4e59eafc6c72b822950aebdc","sha256:3b27b4cca8b9efff4f66fd2b1d5a442b9124f60d222925e46d2027c7bba77476"],"state_sha256":"6cabe4d374ce75e49e52e01c1e821918abfafd3e240713002df0df00a5f71df6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LeSHCqdzYV/MW7NfJaC7K1ORlfr7R3N+nzQdBwj4JfNpY7NtzqjuZh2qIF42RBVhCOFv+3ViwVoPM4/ql/kLDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T10:16:37.920609Z","bundle_sha256":"cd8e1a7ebf0ed996eecae9972a17ac056320a27a011b144d3a7b629af0237490"}}