{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:G4GQ3RYIWEBSPA7IRF6VT3PCAK","short_pith_number":"pith:G4GQ3RYI","canonical_record":{"source":{"id":"1205.0517","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-05-02T18:40:13Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"0551a60f748ebc18eb1b4003786d5072f5b5561f4f5449795513746f5f7c4359","abstract_canon_sha256":"c853afb8d41c79e84550e35c39373cdfd0ad7f57fccc8302aee95d3d88143d94"},"schema_version":"1.0"},"canonical_sha256":"370d0dc708b1032783e8897d59ede202b00269e4438d42dabd7f3db2e0639848","source":{"kind":"arxiv","id":"1205.0517","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.0517","created_at":"2026-05-18T03:41:10Z"},{"alias_kind":"arxiv_version","alias_value":"1205.0517v2","created_at":"2026-05-18T03:41:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.0517","created_at":"2026-05-18T03:41:10Z"},{"alias_kind":"pith_short_12","alias_value":"G4GQ3RYIWEBS","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"G4GQ3RYIWEBSPA7I","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"G4GQ3RYI","created_at":"2026-05-18T12:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:G4GQ3RYIWEBSPA7IRF6VT3PCAK","target":"record","payload":{"canonical_record":{"source":{"id":"1205.0517","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-05-02T18:40:13Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"0551a60f748ebc18eb1b4003786d5072f5b5561f4f5449795513746f5f7c4359","abstract_canon_sha256":"c853afb8d41c79e84550e35c39373cdfd0ad7f57fccc8302aee95d3d88143d94"},"schema_version":"1.0"},"canonical_sha256":"370d0dc708b1032783e8897d59ede202b00269e4438d42dabd7f3db2e0639848","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:10.655724Z","signature_b64":"tFWl49F07lxODNPfVrCxYT29ukoI+dqwgaYdLQnbHk6xI8QfANYFOoSswihnRNdtESwSd7l0MgyTfk4TXeZtCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"370d0dc708b1032783e8897d59ede202b00269e4438d42dabd7f3db2e0639848","last_reissued_at":"2026-05-18T03:41:10.655230Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:10.655230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.0517","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:41:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"82gLxAm3TeKfNzNOBEAUP2d4kC02Xg1m0rH02mdfn81wJal8aT/+trUAhu9eQ2UCEcyUdogWPrXDRVHZNxRSAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:37:28.742327Z"},"content_sha256":"3ab4ded8f2f04c12f3f1677f06fb5b052912b1c692962ebb57f811f13b7bd184","schema_version":"1.0","event_id":"sha256:3ab4ded8f2f04c12f3f1677f06fb5b052912b1c692962ebb57f811f13b7bd184"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:G4GQ3RYIWEBSPA7IRF6VT3PCAK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Mountain-pass algorithm for the quasi-linear Schrodinger equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.NA","authors_text":"Christopher Grumiau, Christophe Troestler, Marco Squassina","submitted_at":"2012-05-02T18:40:13Z","abstract_excerpt":"We discuss the application of the Mountain Pass algorithm to the so-called quasi-linear Schrodinger equation, which is naturally associated with a class of nonsmooth functionals so that the classical algorithm is not directly applicable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0517","kind":"arxiv","version":2},"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":"2026-05-18T03:41:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O8OhiTCw6N3J3AnXJySrfes5udcEHTRo75Q3fTUQB81BAskunRiEGpYHpoDbyLL5hY9C7f0zBSaAk4buI7InAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:37:28.742688Z"},"content_sha256":"38dfe74b8c4757efebbad8917a6e0c57db9ec079e7a1e0d5cfcbcdcb26a105c5","schema_version":"1.0","event_id":"sha256:38dfe74b8c4757efebbad8917a6e0c57db9ec079e7a1e0d5cfcbcdcb26a105c5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G4GQ3RYIWEBSPA7IRF6VT3PCAK/bundle.json","state_url":"https://pith.science/pith/G4GQ3RYIWEBSPA7IRF6VT3PCAK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G4GQ3RYIWEBSPA7IRF6VT3PCAK/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":"2026-05-31T08:37:28Z","links":{"resolver":"https://pith.science/pith/G4GQ3RYIWEBSPA7IRF6VT3PCAK","bundle":"https://pith.science/pith/G4GQ3RYIWEBSPA7IRF6VT3PCAK/bundle.json","state":"https://pith.science/pith/G4GQ3RYIWEBSPA7IRF6VT3PCAK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G4GQ3RYIWEBSPA7IRF6VT3PCAK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:G4GQ3RYIWEBSPA7IRF6VT3PCAK","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":"c853afb8d41c79e84550e35c39373cdfd0ad7f57fccc8302aee95d3d88143d94","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-05-02T18:40:13Z","title_canon_sha256":"0551a60f748ebc18eb1b4003786d5072f5b5561f4f5449795513746f5f7c4359"},"schema_version":"1.0","source":{"id":"1205.0517","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.0517","created_at":"2026-05-18T03:41:10Z"},{"alias_kind":"arxiv_version","alias_value":"1205.0517v2","created_at":"2026-05-18T03:41:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.0517","created_at":"2026-05-18T03:41:10Z"},{"alias_kind":"pith_short_12","alias_value":"G4GQ3RYIWEBS","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"G4GQ3RYIWEBSPA7I","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"G4GQ3RYI","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:38dfe74b8c4757efebbad8917a6e0c57db9ec079e7a1e0d5cfcbcdcb26a105c5","target":"graph","created_at":"2026-05-18T03:41:10Z","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 discuss the application of the Mountain Pass algorithm to the so-called quasi-linear Schrodinger equation, which is naturally associated with a class of nonsmooth functionals so that the classical algorithm is not directly applicable.","authors_text":"Christopher Grumiau, Christophe Troestler, Marco Squassina","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-05-02T18:40:13Z","title":"On the Mountain-pass algorithm for the quasi-linear Schrodinger equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0517","kind":"arxiv","version":2},"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":"sha256:3ab4ded8f2f04c12f3f1677f06fb5b052912b1c692962ebb57f811f13b7bd184","target":"record","created_at":"2026-05-18T03:41:10Z","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":"c853afb8d41c79e84550e35c39373cdfd0ad7f57fccc8302aee95d3d88143d94","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-05-02T18:40:13Z","title_canon_sha256":"0551a60f748ebc18eb1b4003786d5072f5b5561f4f5449795513746f5f7c4359"},"schema_version":"1.0","source":{"id":"1205.0517","kind":"arxiv","version":2}},"canonical_sha256":"370d0dc708b1032783e8897d59ede202b00269e4438d42dabd7f3db2e0639848","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"370d0dc708b1032783e8897d59ede202b00269e4438d42dabd7f3db2e0639848","first_computed_at":"2026-05-18T03:41:10.655230Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:41:10.655230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tFWl49F07lxODNPfVrCxYT29ukoI+dqwgaYdLQnbHk6xI8QfANYFOoSswihnRNdtESwSd7l0MgyTfk4TXeZtCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:41:10.655724Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.0517","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ab4ded8f2f04c12f3f1677f06fb5b052912b1c692962ebb57f811f13b7bd184","sha256:38dfe74b8c4757efebbad8917a6e0c57db9ec079e7a1e0d5cfcbcdcb26a105c5"],"state_sha256":"c266fa15a7f999e459c03b6a97e60e5e270cdc4b9c02a7aaaa4475d79e0a520e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SbXzvpTdhPFNSNqtFi8fSCImGdv1Te2ui3c09qBGMp5wY4aHbJWUVRRKrlaq+MX+3YQAnOokNnCm3ixe/8jqAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T08:37:28.744945Z","bundle_sha256":"a48e8a84c3152fcb49f46aafe37f0fdd8c0794ddb36c5c7627007f462965063e"}}