{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:XE2MB6QHDQZLCDY2RYRIALT325","short_pith_number":"pith:XE2MB6QH","canonical_record":{"source":{"id":"2509.02288","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-09-02T13:08:16Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"05fbddca5aaef999790b7ec4dc8d57e0828baa72b00965f4bb7e3f254d673e75","abstract_canon_sha256":"81fd598a802ee8bed039b0d182f595bf25fb9d8f4d5b5e06ac06cd84efda7fcd"},"schema_version":"1.0"},"canonical_sha256":"b934c0fa071c32b10f1a8e22802e7bd77054618fc0d20518196bb1b742dfa41c","source":{"kind":"arxiv","id":"2509.02288","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.02288","created_at":"2026-07-05T12:03:35Z"},{"alias_kind":"arxiv_version","alias_value":"2509.02288v1","created_at":"2026-07-05T12:03:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.02288","created_at":"2026-07-05T12:03:35Z"},{"alias_kind":"pith_short_12","alias_value":"XE2MB6QHDQZL","created_at":"2026-07-05T12:03:35Z"},{"alias_kind":"pith_short_16","alias_value":"XE2MB6QHDQZLCDY2","created_at":"2026-07-05T12:03:35Z"},{"alias_kind":"pith_short_8","alias_value":"XE2MB6QH","created_at":"2026-07-05T12:03:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:XE2MB6QHDQZLCDY2RYRIALT325","target":"record","payload":{"canonical_record":{"source":{"id":"2509.02288","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-09-02T13:08:16Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"05fbddca5aaef999790b7ec4dc8d57e0828baa72b00965f4bb7e3f254d673e75","abstract_canon_sha256":"81fd598a802ee8bed039b0d182f595bf25fb9d8f4d5b5e06ac06cd84efda7fcd"},"schema_version":"1.0"},"canonical_sha256":"b934c0fa071c32b10f1a8e22802e7bd77054618fc0d20518196bb1b742dfa41c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:03:35.588031Z","signature_b64":"PwCl7oa9ZKzhFqMWbNm8cnuWEsq9wkO7/AhE/igCKjwo+OYtfs4usZMHaUcvaNQbiKGCzWUbubrqu+7Y2MG6Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b934c0fa071c32b10f1a8e22802e7bd77054618fc0d20518196bb1b742dfa41c","last_reissued_at":"2026-07-05T12:03:35.587537Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:03:35.587537Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2509.02288","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":"2026-07-05T12:03:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BDxCriz4pDh1BHvjk5yLRoRaOQmOchSKyhzON97PFJeUrQy4B0D8QJz/Zg049tlVlxn0hEaGZOp/EzFKdTUXCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T01:01:49.412331Z"},"content_sha256":"ef51dc533cc099ffdd9563848cc6956eea33d6db6ef3a2b04042622e8af0a84a","schema_version":"1.0","event_id":"sha256:ef51dc533cc099ffdd9563848cc6956eea33d6db6ef3a2b04042622e8af0a84a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:XE2MB6QHDQZLCDY2RYRIALT325","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Paving the way to a $\\operatorname{T}$-coercive method for the wave equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Carolina Urz\\'ua-Torres, Daniel Hoonhout, Richard L\\\"oscher","submitted_at":"2025-09-02T13:08:16Z","abstract_excerpt":"In this paper, we take a first step toward introducing a space-time transformation operator $\\operatorname{T}$ that establishes $\\operatorname{T}$-coercivity for the weak variational formulation of the wave equation in space and time on bounded Lipschitz domains. As a model problem, we study the ordinary differential equation (ODE) $u'' + \\mu u = f$ for $\\mu>0$, which is linked to the wave equation via a Fourier expansion in space. For its weak formulation, we introduce a transformation operator $\\operatorname{T}_\\mu$ that establishes $\\operatorname{T}_\\mu$-coercivity of the bilinear form yiel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.02288","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/2509.02288/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":"2026-07-05T12:03:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sy538oTNvPx3AOT+U+EDJ2j/CUddwqX3SLvvQ5MJ6E9cIXjMhmlrx72hNO13RC+SDlQySeR+W1liiS2l5J0xBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T01:01:49.412840Z"},"content_sha256":"c7d3e479bea5148c8627aae9161172953d4447cd4a69591db931fbd6e3c7266d","schema_version":"1.0","event_id":"sha256:c7d3e479bea5148c8627aae9161172953d4447cd4a69591db931fbd6e3c7266d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XE2MB6QHDQZLCDY2RYRIALT325/bundle.json","state_url":"https://pith.science/pith/XE2MB6QHDQZLCDY2RYRIALT325/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XE2MB6QHDQZLCDY2RYRIALT325/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":"2026-08-08T01:01:49Z","links":{"resolver":"https://pith.science/pith/XE2MB6QHDQZLCDY2RYRIALT325","bundle":"https://pith.science/pith/XE2MB6QHDQZLCDY2RYRIALT325/bundle.json","state":"https://pith.science/pith/XE2MB6QHDQZLCDY2RYRIALT325/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XE2MB6QHDQZLCDY2RYRIALT325/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:XE2MB6QHDQZLCDY2RYRIALT325","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":"81fd598a802ee8bed039b0d182f595bf25fb9d8f4d5b5e06ac06cd84efda7fcd","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-09-02T13:08:16Z","title_canon_sha256":"05fbddca5aaef999790b7ec4dc8d57e0828baa72b00965f4bb7e3f254d673e75"},"schema_version":"1.0","source":{"id":"2509.02288","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.02288","created_at":"2026-07-05T12:03:35Z"},{"alias_kind":"arxiv_version","alias_value":"2509.02288v1","created_at":"2026-07-05T12:03:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.02288","created_at":"2026-07-05T12:03:35Z"},{"alias_kind":"pith_short_12","alias_value":"XE2MB6QHDQZL","created_at":"2026-07-05T12:03:35Z"},{"alias_kind":"pith_short_16","alias_value":"XE2MB6QHDQZLCDY2","created_at":"2026-07-05T12:03:35Z"},{"alias_kind":"pith_short_8","alias_value":"XE2MB6QH","created_at":"2026-07-05T12:03:35Z"}],"graph_snapshots":[{"event_id":"sha256:c7d3e479bea5148c8627aae9161172953d4447cd4a69591db931fbd6e3c7266d","target":"graph","created_at":"2026-07-05T12:03:35Z","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/2509.02288/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we take a first step toward introducing a space-time transformation operator $\\operatorname{T}$ that establishes $\\operatorname{T}$-coercivity for the weak variational formulation of the wave equation in space and time on bounded Lipschitz domains. As a model problem, we study the ordinary differential equation (ODE) $u'' + \\mu u = f$ for $\\mu>0$, which is linked to the wave equation via a Fourier expansion in space. For its weak formulation, we introduce a transformation operator $\\operatorname{T}_\\mu$ that establishes $\\operatorname{T}_\\mu$-coercivity of the bilinear form yiel","authors_text":"Carolina Urz\\'ua-Torres, Daniel Hoonhout, Richard L\\\"oscher","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-09-02T13:08:16Z","title":"Paving the way to a $\\operatorname{T}$-coercive method for the wave equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.02288","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:ef51dc533cc099ffdd9563848cc6956eea33d6db6ef3a2b04042622e8af0a84a","target":"record","created_at":"2026-07-05T12:03:35Z","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":"81fd598a802ee8bed039b0d182f595bf25fb9d8f4d5b5e06ac06cd84efda7fcd","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-09-02T13:08:16Z","title_canon_sha256":"05fbddca5aaef999790b7ec4dc8d57e0828baa72b00965f4bb7e3f254d673e75"},"schema_version":"1.0","source":{"id":"2509.02288","kind":"arxiv","version":1}},"canonical_sha256":"b934c0fa071c32b10f1a8e22802e7bd77054618fc0d20518196bb1b742dfa41c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b934c0fa071c32b10f1a8e22802e7bd77054618fc0d20518196bb1b742dfa41c","first_computed_at":"2026-07-05T12:03:35.587537Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:03:35.587537Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PwCl7oa9ZKzhFqMWbNm8cnuWEsq9wkO7/AhE/igCKjwo+OYtfs4usZMHaUcvaNQbiKGCzWUbubrqu+7Y2MG6Cg==","signature_status":"signed_v1","signed_at":"2026-07-05T12:03:35.588031Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.02288","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef51dc533cc099ffdd9563848cc6956eea33d6db6ef3a2b04042622e8af0a84a","sha256:c7d3e479bea5148c8627aae9161172953d4447cd4a69591db931fbd6e3c7266d"],"state_sha256":"df6462a224147eca137ca7d27da4cebcc62fd8c1993076831e0dfe225b11d508"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GY9pCx9QStz6jKiPnWd4wJSwILiG36eZQ1FUaLlit8MR/ZIpexcfR7DEOqJX/0wq4XS90q/MdAgkyA5WXvQ4Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T01:01:49.416901Z","bundle_sha256":"864a381a6c08705f21812ebccc0077041c0baf6f0f2a11245a1fb77a210009c9"}}