{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:JHXUZDHC7KUYH6CVSKF3MJIEMP","short_pith_number":"pith:JHXUZDHC","canonical_record":{"source":{"id":"1111.2177","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2011-11-09T11:33:57Z","cross_cats_sorted":[],"title_canon_sha256":"762c477c3dad1ab94d532c1d1d1300ccea74d55b0a0a1ef9d9a5733f98aefa9c","abstract_canon_sha256":"64debc86a219c96746e47389fd2c59dc2e68e52c633dcc67c27220ab689de145"},"schema_version":"1.0"},"canonical_sha256":"49ef4c8ce2faa983f855928bb6250463c6ae7dd500a75724d01b29bfc8f6ba5d","source":{"kind":"arxiv","id":"1111.2177","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.2177","created_at":"2026-05-18T03:37:09Z"},{"alias_kind":"arxiv_version","alias_value":"1111.2177v1","created_at":"2026-05-18T03:37:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.2177","created_at":"2026-05-18T03:37:09Z"},{"alias_kind":"pith_short_12","alias_value":"JHXUZDHC7KUY","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JHXUZDHC7KUYH6CV","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JHXUZDHC","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:JHXUZDHC7KUYH6CVSKF3MJIEMP","target":"record","payload":{"canonical_record":{"source":{"id":"1111.2177","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2011-11-09T11:33:57Z","cross_cats_sorted":[],"title_canon_sha256":"762c477c3dad1ab94d532c1d1d1300ccea74d55b0a0a1ef9d9a5733f98aefa9c","abstract_canon_sha256":"64debc86a219c96746e47389fd2c59dc2e68e52c633dcc67c27220ab689de145"},"schema_version":"1.0"},"canonical_sha256":"49ef4c8ce2faa983f855928bb6250463c6ae7dd500a75724d01b29bfc8f6ba5d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:37:09.037226Z","signature_b64":"jJOtucQhR4c+YntQXFEj4Y1fOrqn4qP22hLx8ZwZMrmpxT4318/BMNbb9NyIijjWDgM4z7Xg1IjWbS0xhPoOAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"49ef4c8ce2faa983f855928bb6250463c6ae7dd500a75724d01b29bfc8f6ba5d","last_reissued_at":"2026-05-18T03:37:09.036476Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:37:09.036476Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.2177","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":"2026-05-18T03:37:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5s5gSSjaZ5hOkdHr4UxRpt9X5yxue7BzAlysSQhO+N0stgtL0euEZxlLxeKDNUnrChFY9r1i+Pet4yuJAu0EAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T12:02:59.095824Z"},"content_sha256":"f044633811ee8406c7883b17da2100277093608f91e3e49ff8eda37b1ac2a71b","schema_version":"1.0","event_id":"sha256:f044633811ee8406c7883b17da2100277093608f91e3e49ff8eda37b1ac2a71b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:JHXUZDHC7KUYH6CVSKF3MJIEMP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Numerical stability of the Z4c formulation of general relativity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"David Hilditch, Zhoujian Cao","submitted_at":"2011-11-09T11:33:57Z","abstract_excerpt":"We study numerical stability of different approaches to the discretization of a conformal decomposition of the Z4 formulation of general relativity. We demonstrate that in the linear, constant coefficient regime a novel discretization for tensors is formally numerically stable with a method of lines time-integrator. We then perform a full set of apples with apples tests on the non-linear system, and thus present numerical evidence that both the new and standard discretizations are, in some sense, numerically stable in the non-linear regime. The results of the Z4c numerical tests are compared w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2177","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":"2026-05-18T03:37:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v4d2aIQmAHC4FTSB8j+LZjYwkCgZ4+MWDbMaxzkCNwQhr/fchhj2qUTpg+dVL6nDo6AyFuDQKPsxr8ryTiajDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T12:02:59.096461Z"},"content_sha256":"4b05d7dfdba9dd5569849eaa94a161df5c399ff28baa5006b790fec467bc3e02","schema_version":"1.0","event_id":"sha256:4b05d7dfdba9dd5569849eaa94a161df5c399ff28baa5006b790fec467bc3e02"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JHXUZDHC7KUYH6CVSKF3MJIEMP/bundle.json","state_url":"https://pith.science/pith/JHXUZDHC7KUYH6CVSKF3MJIEMP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JHXUZDHC7KUYH6CVSKF3MJIEMP/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":"2026-06-08T12:02:59Z","links":{"resolver":"https://pith.science/pith/JHXUZDHC7KUYH6CVSKF3MJIEMP","bundle":"https://pith.science/pith/JHXUZDHC7KUYH6CVSKF3MJIEMP/bundle.json","state":"https://pith.science/pith/JHXUZDHC7KUYH6CVSKF3MJIEMP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JHXUZDHC7KUYH6CVSKF3MJIEMP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:JHXUZDHC7KUYH6CVSKF3MJIEMP","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":"64debc86a219c96746e47389fd2c59dc2e68e52c633dcc67c27220ab689de145","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2011-11-09T11:33:57Z","title_canon_sha256":"762c477c3dad1ab94d532c1d1d1300ccea74d55b0a0a1ef9d9a5733f98aefa9c"},"schema_version":"1.0","source":{"id":"1111.2177","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.2177","created_at":"2026-05-18T03:37:09Z"},{"alias_kind":"arxiv_version","alias_value":"1111.2177v1","created_at":"2026-05-18T03:37:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.2177","created_at":"2026-05-18T03:37:09Z"},{"alias_kind":"pith_short_12","alias_value":"JHXUZDHC7KUY","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JHXUZDHC7KUYH6CV","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JHXUZDHC","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:4b05d7dfdba9dd5569849eaa94a161df5c399ff28baa5006b790fec467bc3e02","target":"graph","created_at":"2026-05-18T03:37:09Z","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":"We study numerical stability of different approaches to the discretization of a conformal decomposition of the Z4 formulation of general relativity. We demonstrate that in the linear, constant coefficient regime a novel discretization for tensors is formally numerically stable with a method of lines time-integrator. We then perform a full set of apples with apples tests on the non-linear system, and thus present numerical evidence that both the new and standard discretizations are, in some sense, numerically stable in the non-linear regime. The results of the Z4c numerical tests are compared w","authors_text":"David Hilditch, Zhoujian Cao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2011-11-09T11:33:57Z","title":"Numerical stability of the Z4c formulation of general relativity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2177","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:f044633811ee8406c7883b17da2100277093608f91e3e49ff8eda37b1ac2a71b","target":"record","created_at":"2026-05-18T03:37:09Z","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":"64debc86a219c96746e47389fd2c59dc2e68e52c633dcc67c27220ab689de145","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2011-11-09T11:33:57Z","title_canon_sha256":"762c477c3dad1ab94d532c1d1d1300ccea74d55b0a0a1ef9d9a5733f98aefa9c"},"schema_version":"1.0","source":{"id":"1111.2177","kind":"arxiv","version":1}},"canonical_sha256":"49ef4c8ce2faa983f855928bb6250463c6ae7dd500a75724d01b29bfc8f6ba5d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"49ef4c8ce2faa983f855928bb6250463c6ae7dd500a75724d01b29bfc8f6ba5d","first_computed_at":"2026-05-18T03:37:09.036476Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:09.036476Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jJOtucQhR4c+YntQXFEj4Y1fOrqn4qP22hLx8ZwZMrmpxT4318/BMNbb9NyIijjWDgM4z7Xg1IjWbS0xhPoOAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:09.037226Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.2177","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f044633811ee8406c7883b17da2100277093608f91e3e49ff8eda37b1ac2a71b","sha256:4b05d7dfdba9dd5569849eaa94a161df5c399ff28baa5006b790fec467bc3e02"],"state_sha256":"40c32d6a605d96ef50a677d1e270871a2b6feff4a528bfb0860eb25e0eb43a73"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RdAZN72LatmDGhLgTMxI3TVo/V3KPYYpP2AeoZVKLaU3fBs7AbZFRQgmq8JGofOmeFD0MYQ1oDw8v4YNA+gbDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T12:02:59.098759Z","bundle_sha256":"c3fcca9c47983cafb20e932c1eed2461b05d4129716d09f63857c1b601794c0d"}}