{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:QFEDV2P6THIU2CPWH3HP5DPQYO","short_pith_number":"pith:QFEDV2P6","canonical_record":{"source":{"id":"2407.07130","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-07-09T11:26:21Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"fd719fae36c8d791f05782d673c830bb6895b1b560db3690af5d375af319b327","abstract_canon_sha256":"8aa1aff86bffc42c44397669d2169b52f33d5263c5d11a9a91a3b04c48bcd779"},"schema_version":"1.0"},"canonical_sha256":"81483ae9fe99d14d09f63ecefe8df0c38d1b258b97aa0ae4133fd848410150e9","source":{"kind":"arxiv","id":"2407.07130","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.07130","created_at":"2026-07-05T08:58:25Z"},{"alias_kind":"arxiv_version","alias_value":"2407.07130v2","created_at":"2026-07-05T08:58:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.07130","created_at":"2026-07-05T08:58:25Z"},{"alias_kind":"pith_short_12","alias_value":"QFEDV2P6THIU","created_at":"2026-07-05T08:58:25Z"},{"alias_kind":"pith_short_16","alias_value":"QFEDV2P6THIU2CPW","created_at":"2026-07-05T08:58:25Z"},{"alias_kind":"pith_short_8","alias_value":"QFEDV2P6","created_at":"2026-07-05T08:58:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:QFEDV2P6THIU2CPWH3HP5DPQYO","target":"record","payload":{"canonical_record":{"source":{"id":"2407.07130","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-07-09T11:26:21Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"fd719fae36c8d791f05782d673c830bb6895b1b560db3690af5d375af319b327","abstract_canon_sha256":"8aa1aff86bffc42c44397669d2169b52f33d5263c5d11a9a91a3b04c48bcd779"},"schema_version":"1.0"},"canonical_sha256":"81483ae9fe99d14d09f63ecefe8df0c38d1b258b97aa0ae4133fd848410150e9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:58:25.114576Z","signature_b64":"xPbCsQsW74wZajSE1mTgKyzggqO4XYuj9Z/wpoubDNzxric6jeXoi8sHJ0Jb8SiST/y/PiU581x9kvh0VY45Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81483ae9fe99d14d09f63ecefe8df0c38d1b258b97aa0ae4133fd848410150e9","last_reissued_at":"2026-07-05T08:58:25.114082Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:58:25.114082Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2407.07130","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":"2026-07-05T08:58:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PE/8lUg8/tqLGClqtumU/pOnansw8yh1dSmLaX+B4UXzlJoI81+Orf0RTOS/kcpmOODCzWvIlYS81nReyLavBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T21:27:15.599956Z"},"content_sha256":"205daf6027a91cd3a74b7e0d0bcce26f98b625ef589c5e862ecc8da788c4a189","schema_version":"1.0","event_id":"sha256:205daf6027a91cd3a74b7e0d0bcce26f98b625ef589c5e862ecc8da788c4a189"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:QFEDV2P6THIU2CPWH3HP5DPQYO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Minimal surfaces and alternating multiple zetas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DG","authors_text":"Lynn Heller, Martin Traizet, Sebastian Heller, Steven Charlton","submitted_at":"2024-07-09T11:26:21Z","abstract_excerpt":"In this paper we show for every sufficiently large integer $g$ the existence of a complete family of closed and embedded constant mean curvature (CMC) surfaces deforming the Lawson surfaces $\\xi_{1,g}$ parametrized by their conformal type. When specializing to the minimal case, we discover a pattern resulting in the coefficients of the involved expansions being alternating multiple zeta values (MZVs), which generalizes the notion of Riemann's zeta values to multiple integer variables. This allows us to extend a new existence proof of the Lawson surfaces $\\xi_{1,g}$ to all $g\\geq 3$ using compl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.07130","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.07130/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":"2026-07-05T08:58:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bq1xMMw2VIY0NOJgEPLMcAM8BkmzpTKYWmIXMSIRVc6psMHJq0ia432Kb/bLcuftj7mUOxoi1U6TorarFXazCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T21:27:15.600451Z"},"content_sha256":"af07408e1d0dbc349f367bf91918b4f069ce669f421bebdaae3b492805d24ab6","schema_version":"1.0","event_id":"sha256:af07408e1d0dbc349f367bf91918b4f069ce669f421bebdaae3b492805d24ab6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QFEDV2P6THIU2CPWH3HP5DPQYO/bundle.json","state_url":"https://pith.science/pith/QFEDV2P6THIU2CPWH3HP5DPQYO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QFEDV2P6THIU2CPWH3HP5DPQYO/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":"2026-08-08T21:27:15Z","links":{"resolver":"https://pith.science/pith/QFEDV2P6THIU2CPWH3HP5DPQYO","bundle":"https://pith.science/pith/QFEDV2P6THIU2CPWH3HP5DPQYO/bundle.json","state":"https://pith.science/pith/QFEDV2P6THIU2CPWH3HP5DPQYO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QFEDV2P6THIU2CPWH3HP5DPQYO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:QFEDV2P6THIU2CPWH3HP5DPQYO","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":"8aa1aff86bffc42c44397669d2169b52f33d5263c5d11a9a91a3b04c48bcd779","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-07-09T11:26:21Z","title_canon_sha256":"fd719fae36c8d791f05782d673c830bb6895b1b560db3690af5d375af319b327"},"schema_version":"1.0","source":{"id":"2407.07130","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.07130","created_at":"2026-07-05T08:58:25Z"},{"alias_kind":"arxiv_version","alias_value":"2407.07130v2","created_at":"2026-07-05T08:58:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.07130","created_at":"2026-07-05T08:58:25Z"},{"alias_kind":"pith_short_12","alias_value":"QFEDV2P6THIU","created_at":"2026-07-05T08:58:25Z"},{"alias_kind":"pith_short_16","alias_value":"QFEDV2P6THIU2CPW","created_at":"2026-07-05T08:58:25Z"},{"alias_kind":"pith_short_8","alias_value":"QFEDV2P6","created_at":"2026-07-05T08:58:25Z"}],"graph_snapshots":[{"event_id":"sha256:af07408e1d0dbc349f367bf91918b4f069ce669f421bebdaae3b492805d24ab6","target":"graph","created_at":"2026-07-05T08:58:25Z","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/2407.07130/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we show for every sufficiently large integer $g$ the existence of a complete family of closed and embedded constant mean curvature (CMC) surfaces deforming the Lawson surfaces $\\xi_{1,g}$ parametrized by their conformal type. When specializing to the minimal case, we discover a pattern resulting in the coefficients of the involved expansions being alternating multiple zeta values (MZVs), which generalizes the notion of Riemann's zeta values to multiple integer variables. This allows us to extend a new existence proof of the Lawson surfaces $\\xi_{1,g}$ to all $g\\geq 3$ using compl","authors_text":"Lynn Heller, Martin Traizet, Sebastian Heller, Steven Charlton","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-07-09T11:26:21Z","title":"Minimal surfaces and alternating multiple zetas"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.07130","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":"sha256:205daf6027a91cd3a74b7e0d0bcce26f98b625ef589c5e862ecc8da788c4a189","target":"record","created_at":"2026-07-05T08:58:25Z","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":"8aa1aff86bffc42c44397669d2169b52f33d5263c5d11a9a91a3b04c48bcd779","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-07-09T11:26:21Z","title_canon_sha256":"fd719fae36c8d791f05782d673c830bb6895b1b560db3690af5d375af319b327"},"schema_version":"1.0","source":{"id":"2407.07130","kind":"arxiv","version":2}},"canonical_sha256":"81483ae9fe99d14d09f63ecefe8df0c38d1b258b97aa0ae4133fd848410150e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81483ae9fe99d14d09f63ecefe8df0c38d1b258b97aa0ae4133fd848410150e9","first_computed_at":"2026-07-05T08:58:25.114082Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:58:25.114082Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xPbCsQsW74wZajSE1mTgKyzggqO4XYuj9Z/wpoubDNzxric6jeXoi8sHJ0Jb8SiST/y/PiU581x9kvh0VY45Cw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:58:25.114576Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.07130","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:205daf6027a91cd3a74b7e0d0bcce26f98b625ef589c5e862ecc8da788c4a189","sha256:af07408e1d0dbc349f367bf91918b4f069ce669f421bebdaae3b492805d24ab6"],"state_sha256":"76721e29bcd094a30eae2737a0938a90c28b097994dcc2aa30db988f1c3cb950"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FTfWSriXRS/k+e5dMEpLPiDp+E03+y4JmdF5tS9f20nDhwpm/xyuNc6c7EZlmIlZ3gBN3VmFlomIZqN/q+meBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T21:27:15.605334Z","bundle_sha256":"7d7a49d788dd4d36ea9f9930b52760ce7dbc5ffda8d8fb9c407f15a31c92eadf"}}