{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:VP3HLO33Z7IKHDRKAHY3FMASQQ","short_pith_number":"pith:VP3HLO33","canonical_record":{"source":{"id":"math/0701681","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"2007-01-24T14:24:28Z","cross_cats_sorted":[],"title_canon_sha256":"447c44e1b829d24b890dad3841885a02d4ecd2f51f2347bae1356065b847a823","abstract_canon_sha256":"7d2602b35a7c2b2cf2865f74a55b43489223667164238d7ef5a2d82c8fc8d86a"},"schema_version":"1.0"},"canonical_sha256":"abf675bb7bcfd0a38e2a01f1b2b012842e42e2d95d1bbc8c0e0280f4b674142b","source":{"kind":"arxiv","id":"math/0701681","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0701681","created_at":"2026-05-18T00:19:54Z"},{"alias_kind":"arxiv_version","alias_value":"math/0701681v1","created_at":"2026-05-18T00:19:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0701681","created_at":"2026-05-18T00:19:54Z"},{"alias_kind":"pith_short_12","alias_value":"VP3HLO33Z7IK","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"VP3HLO33Z7IKHDRK","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"VP3HLO33","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:VP3HLO33Z7IKHDRKAHY3FMASQQ","target":"record","payload":{"canonical_record":{"source":{"id":"math/0701681","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"2007-01-24T14:24:28Z","cross_cats_sorted":[],"title_canon_sha256":"447c44e1b829d24b890dad3841885a02d4ecd2f51f2347bae1356065b847a823","abstract_canon_sha256":"7d2602b35a7c2b2cf2865f74a55b43489223667164238d7ef5a2d82c8fc8d86a"},"schema_version":"1.0"},"canonical_sha256":"abf675bb7bcfd0a38e2a01f1b2b012842e42e2d95d1bbc8c0e0280f4b674142b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:54.153624Z","signature_b64":"s7JGZabsu/IbnGt7h35PyquzYk0vr9Ad9urc5ZY2JxRksWkQtO7PowKLSU2yxDTRaAv1NQFpDMFn2YKrugq5Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"abf675bb7bcfd0a38e2a01f1b2b012842e42e2d95d1bbc8c0e0280f4b674142b","last_reissued_at":"2026-05-18T00:19:54.152877Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:54.152877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0701681","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":"2026-05-18T00:19:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Cd2yY8O7fAWYG7PvjKAMUggNBN3M/vDm9AwHse7FNsksEZi4++1UJQIqxWsvPJid6Lbt9La2mN9vJ/XdNStFDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T04:22:03.965133Z"},"content_sha256":"8f70e802e4641b9226d88dde55ac0646ef672323b8469a1207fe982906d4735a","schema_version":"1.0","event_id":"sha256:8f70e802e4641b9226d88dde55ac0646ef672323b8469a1207fe982906d4735a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:VP3HLO33Z7IKHDRKAHY3FMASQQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Nash-Moser theorem for singular evolution equations. Application to the Serre and Green-Naghdi equations","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Borys Alvarez-Samaniego (IMB), David Lannes (IMB)","submitted_at":"2007-01-24T14:24:28Z","abstract_excerpt":"We study the well-posedness of the initial value problem for a wide class of singular evolution equations. We prove a general well-posedness theorem under three assumptions easy to check: the first controls the singular part of the equation, the second the behavior of the nonlinearities, and the third one assumes that an energy estimate can be found for the linearized system. We allow losses of derivatives in this energy estimate and therefore construct a solution by a Nash-Moser iterative scheme. As an application to this general theorem, we prove the well-posedness of the Serre and Green-Nag"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0701681","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":"2026-05-18T00:19:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"699VEA3hRSZ0F01vhnzJ6IF+B5yvgH+B3wlGOvxeeEiyfBxbwUHmxnpYelYEvoWQrEKkcPisv9XsU0l1jAM5Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T04:22:03.965497Z"},"content_sha256":"ca8461424c9e59f01a0312a7ed0a74f8435f4fead46a0c849539a4de53afb9bc","schema_version":"1.0","event_id":"sha256:ca8461424c9e59f01a0312a7ed0a74f8435f4fead46a0c849539a4de53afb9bc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VP3HLO33Z7IKHDRKAHY3FMASQQ/bundle.json","state_url":"https://pith.science/pith/VP3HLO33Z7IKHDRKAHY3FMASQQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VP3HLO33Z7IKHDRKAHY3FMASQQ/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":"2026-06-04T04:22:03Z","links":{"resolver":"https://pith.science/pith/VP3HLO33Z7IKHDRKAHY3FMASQQ","bundle":"https://pith.science/pith/VP3HLO33Z7IKHDRKAHY3FMASQQ/bundle.json","state":"https://pith.science/pith/VP3HLO33Z7IKHDRKAHY3FMASQQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VP3HLO33Z7IKHDRKAHY3FMASQQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:VP3HLO33Z7IKHDRKAHY3FMASQQ","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":"7d2602b35a7c2b2cf2865f74a55b43489223667164238d7ef5a2d82c8fc8d86a","cross_cats_sorted":[],"license":"","primary_cat":"math.AP","submitted_at":"2007-01-24T14:24:28Z","title_canon_sha256":"447c44e1b829d24b890dad3841885a02d4ecd2f51f2347bae1356065b847a823"},"schema_version":"1.0","source":{"id":"math/0701681","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0701681","created_at":"2026-05-18T00:19:54Z"},{"alias_kind":"arxiv_version","alias_value":"math/0701681v1","created_at":"2026-05-18T00:19:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0701681","created_at":"2026-05-18T00:19:54Z"},{"alias_kind":"pith_short_12","alias_value":"VP3HLO33Z7IK","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"VP3HLO33Z7IKHDRK","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"VP3HLO33","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:ca8461424c9e59f01a0312a7ed0a74f8435f4fead46a0c849539a4de53afb9bc","target":"graph","created_at":"2026-05-18T00:19:54Z","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 the well-posedness of the initial value problem for a wide class of singular evolution equations. We prove a general well-posedness theorem under three assumptions easy to check: the first controls the singular part of the equation, the second the behavior of the nonlinearities, and the third one assumes that an energy estimate can be found for the linearized system. We allow losses of derivatives in this energy estimate and therefore construct a solution by a Nash-Moser iterative scheme. As an application to this general theorem, we prove the well-posedness of the Serre and Green-Nag","authors_text":"Borys Alvarez-Samaniego (IMB), David Lannes (IMB)","cross_cats":[],"headline":"","license":"","primary_cat":"math.AP","submitted_at":"2007-01-24T14:24:28Z","title":"A Nash-Moser theorem for singular evolution equations. Application to the Serre and Green-Naghdi equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0701681","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":"sha256:8f70e802e4641b9226d88dde55ac0646ef672323b8469a1207fe982906d4735a","target":"record","created_at":"2026-05-18T00:19:54Z","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":"7d2602b35a7c2b2cf2865f74a55b43489223667164238d7ef5a2d82c8fc8d86a","cross_cats_sorted":[],"license":"","primary_cat":"math.AP","submitted_at":"2007-01-24T14:24:28Z","title_canon_sha256":"447c44e1b829d24b890dad3841885a02d4ecd2f51f2347bae1356065b847a823"},"schema_version":"1.0","source":{"id":"math/0701681","kind":"arxiv","version":1}},"canonical_sha256":"abf675bb7bcfd0a38e2a01f1b2b012842e42e2d95d1bbc8c0e0280f4b674142b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"abf675bb7bcfd0a38e2a01f1b2b012842e42e2d95d1bbc8c0e0280f4b674142b","first_computed_at":"2026-05-18T00:19:54.152877Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:54.152877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s7JGZabsu/IbnGt7h35PyquzYk0vr9Ad9urc5ZY2JxRksWkQtO7PowKLSU2yxDTRaAv1NQFpDMFn2YKrugq5Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:54.153624Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0701681","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f70e802e4641b9226d88dde55ac0646ef672323b8469a1207fe982906d4735a","sha256:ca8461424c9e59f01a0312a7ed0a74f8435f4fead46a0c849539a4de53afb9bc"],"state_sha256":"8c48fd8ababd787cd3b1b57439ee9735d4c4b29a86424cff11787f76c7cbba0e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X6oyzgh1ZtRvcIHcyrsFmMqfRmdU8Z0kv7cqVT9LUQV6lpHn/2r/KyM46iVbdsJlI6RIvRBNyalrX5AzaVWdDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T04:22:03.967442Z","bundle_sha256":"d5b98c5571c8fe15bd6dd45fbc65725501bc4adef67ff9a06ac20140eb8abb8f"}}