{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:GCHP3SS7Q6PQWIAUN46B7BLWEB","short_pith_number":"pith:GCHP3SS7","canonical_record":{"source":{"id":"2607.02257","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-02T14:45:34Z","cross_cats_sorted":[],"title_canon_sha256":"9a98e005e5dc1b647674808e9d167f20796cf0f81acb08758264d5f6731c58d1","abstract_canon_sha256":"aad26b8098671f00684c4965a3ad3e280b2e53ddba9bde3a00bf8707d7108037"},"schema_version":"1.0"},"canonical_sha256":"308efdca5f879f0b20146f3c1f857620463b2afddb97d2ed2ad215cc6241cd52","source":{"kind":"arxiv","id":"2607.02257","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.02257","created_at":"2026-07-03T01:17:46Z"},{"alias_kind":"arxiv_version","alias_value":"2607.02257v1","created_at":"2026-07-03T01:17:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.02257","created_at":"2026-07-03T01:17:46Z"},{"alias_kind":"pith_short_12","alias_value":"GCHP3SS7Q6PQ","created_at":"2026-07-03T01:17:46Z"},{"alias_kind":"pith_short_16","alias_value":"GCHP3SS7Q6PQWIAU","created_at":"2026-07-03T01:17:46Z"},{"alias_kind":"pith_short_8","alias_value":"GCHP3SS7","created_at":"2026-07-03T01:17:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:GCHP3SS7Q6PQWIAUN46B7BLWEB","target":"record","payload":{"canonical_record":{"source":{"id":"2607.02257","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-02T14:45:34Z","cross_cats_sorted":[],"title_canon_sha256":"9a98e005e5dc1b647674808e9d167f20796cf0f81acb08758264d5f6731c58d1","abstract_canon_sha256":"aad26b8098671f00684c4965a3ad3e280b2e53ddba9bde3a00bf8707d7108037"},"schema_version":"1.0"},"canonical_sha256":"308efdca5f879f0b20146f3c1f857620463b2afddb97d2ed2ad215cc6241cd52","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-03T01:17:46.744857Z","signature_b64":"DlzkILDIiC8p6rVeYgzpyvu+jNbrufCm9hQIPYTbpQnGHSU7TBbKWigxczi6euyHeuu9FmqTY+1ZbzuptXJfAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"308efdca5f879f0b20146f3c1f857620463b2afddb97d2ed2ad215cc6241cd52","last_reissued_at":"2026-07-03T01:17:46.744440Z","signature_status":"signed_v1","first_computed_at":"2026-07-03T01:17:46.744440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.02257","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":"2026-07-03T01:17:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3Exc9zMnHhnPXzxdXsmt2ZLEfazBdvkBJR9Oj1h8xZ5wM+D0T7c8WH2hkXIPpD8ZFh0c1z1YEXa5cKPgIqk/AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T09:19:50.918461Z"},"content_sha256":"a4f73011d30751bb28aadfde938cc7c5e03dc7a373e447a43bbd68e16c77e95f","schema_version":"1.0","event_id":"sha256:a4f73011d30751bb28aadfde938cc7c5e03dc7a373e447a43bbd68e16c77e95f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:GCHP3SS7Q6PQWIAUN46B7BLWEB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global well--posedness for the mass--critical nonlinear Schr{\\\"o}dinger equation on $\\mathbb{T}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Benjamin Dodson","submitted_at":"2026-07-02T14:45:34Z","abstract_excerpt":"We prove a global well--posedness result for the quintic NLS on $\\mathbb{T}$ for initial data in $H^{s}(\\mathbb{T})$, $s > 1/3$. This improves the previous best bound of $s > 2/5$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.02257","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/2607.02257/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":"2026-07-03T01:17:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dNL/2bVTIOBbYZBktR5LYMKLIGWa96lX7aOYRDJBZO9bh5glyFsKUmrvM7sUH5jYte9xehxzjPAA8NAwRhwvCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T09:19:50.918832Z"},"content_sha256":"0ee7cebd46e1d5e575e0140c7863fb0cf8b999b6c5f0b05aba39e49dcdb28ff9","schema_version":"1.0","event_id":"sha256:0ee7cebd46e1d5e575e0140c7863fb0cf8b999b6c5f0b05aba39e49dcdb28ff9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GCHP3SS7Q6PQWIAUN46B7BLWEB/bundle.json","state_url":"https://pith.science/pith/GCHP3SS7Q6PQWIAUN46B7BLWEB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GCHP3SS7Q6PQWIAUN46B7BLWEB/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":"2026-07-07T09:19:50Z","links":{"resolver":"https://pith.science/pith/GCHP3SS7Q6PQWIAUN46B7BLWEB","bundle":"https://pith.science/pith/GCHP3SS7Q6PQWIAUN46B7BLWEB/bundle.json","state":"https://pith.science/pith/GCHP3SS7Q6PQWIAUN46B7BLWEB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GCHP3SS7Q6PQWIAUN46B7BLWEB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:GCHP3SS7Q6PQWIAUN46B7BLWEB","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":"aad26b8098671f00684c4965a3ad3e280b2e53ddba9bde3a00bf8707d7108037","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-02T14:45:34Z","title_canon_sha256":"9a98e005e5dc1b647674808e9d167f20796cf0f81acb08758264d5f6731c58d1"},"schema_version":"1.0","source":{"id":"2607.02257","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.02257","created_at":"2026-07-03T01:17:46Z"},{"alias_kind":"arxiv_version","alias_value":"2607.02257v1","created_at":"2026-07-03T01:17:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.02257","created_at":"2026-07-03T01:17:46Z"},{"alias_kind":"pith_short_12","alias_value":"GCHP3SS7Q6PQ","created_at":"2026-07-03T01:17:46Z"},{"alias_kind":"pith_short_16","alias_value":"GCHP3SS7Q6PQWIAU","created_at":"2026-07-03T01:17:46Z"},{"alias_kind":"pith_short_8","alias_value":"GCHP3SS7","created_at":"2026-07-03T01:17:46Z"}],"graph_snapshots":[{"event_id":"sha256:0ee7cebd46e1d5e575e0140c7863fb0cf8b999b6c5f0b05aba39e49dcdb28ff9","target":"graph","created_at":"2026-07-03T01:17:46Z","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/2607.02257/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove a global well--posedness result for the quintic NLS on $\\mathbb{T}$ for initial data in $H^{s}(\\mathbb{T})$, $s > 1/3$. This improves the previous best bound of $s > 2/5$.","authors_text":"Benjamin Dodson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-02T14:45:34Z","title":"Global well--posedness for the mass--critical nonlinear Schr{\\\"o}dinger equation on $\\mathbb{T}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.02257","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:a4f73011d30751bb28aadfde938cc7c5e03dc7a373e447a43bbd68e16c77e95f","target":"record","created_at":"2026-07-03T01:17:46Z","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":"aad26b8098671f00684c4965a3ad3e280b2e53ddba9bde3a00bf8707d7108037","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-02T14:45:34Z","title_canon_sha256":"9a98e005e5dc1b647674808e9d167f20796cf0f81acb08758264d5f6731c58d1"},"schema_version":"1.0","source":{"id":"2607.02257","kind":"arxiv","version":1}},"canonical_sha256":"308efdca5f879f0b20146f3c1f857620463b2afddb97d2ed2ad215cc6241cd52","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"308efdca5f879f0b20146f3c1f857620463b2afddb97d2ed2ad215cc6241cd52","first_computed_at":"2026-07-03T01:17:46.744440Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-03T01:17:46.744440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DlzkILDIiC8p6rVeYgzpyvu+jNbrufCm9hQIPYTbpQnGHSU7TBbKWigxczi6euyHeuu9FmqTY+1ZbzuptXJfAA==","signature_status":"signed_v1","signed_at":"2026-07-03T01:17:46.744857Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.02257","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4f73011d30751bb28aadfde938cc7c5e03dc7a373e447a43bbd68e16c77e95f","sha256:0ee7cebd46e1d5e575e0140c7863fb0cf8b999b6c5f0b05aba39e49dcdb28ff9"],"state_sha256":"a639334dd56ba634b9c016a4bc5c1ab8fc7f691ecd6ed2f738e165b4b9d51722"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TRLK/M/9IqMzL0w7iCigJawZuUEirRhetWEdWqekIy97TlyQdhQG2zFqLEdiv+h5D5AD80R6os2KAwXFZStMAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T09:19:50.920802Z","bundle_sha256":"7f72ee3e0833ad1346facff79bfd17fa27dac6496b5bb69a2af7fd2d06e35d69"}}