{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:V5K5NRPAMVDOBUYKNVO44Y3YXV","short_pith_number":"pith:V5K5NRPA","canonical_record":{"source":{"id":"2605.12834","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-13T00:04:50Z","cross_cats_sorted":[],"title_canon_sha256":"ec5c3ce6ed1ca13a65df209f2e610a6c495bb9f28255c24666b10faa8444ac32","abstract_canon_sha256":"349c1b38caaeba84ee134ad3aac10cac106c11364d1d453a8cf706a5fa114315"},"schema_version":"1.0"},"canonical_sha256":"af55d6c5e06546e0d30a6d5dce6378bd54d173ae5bbd0a7a357d694f03116d66","source":{"kind":"arxiv","id":"2605.12834","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.12834","created_at":"2026-05-18T03:09:12Z"},{"alias_kind":"arxiv_version","alias_value":"2605.12834v1","created_at":"2026-05-18T03:09:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.12834","created_at":"2026-05-18T03:09:12Z"},{"alias_kind":"pith_short_12","alias_value":"V5K5NRPAMVDO","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"V5K5NRPAMVDOBUYK","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"V5K5NRPA","created_at":"2026-05-18T12:33:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:V5K5NRPAMVDOBUYKNVO44Y3YXV","target":"record","payload":{"canonical_record":{"source":{"id":"2605.12834","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-13T00:04:50Z","cross_cats_sorted":[],"title_canon_sha256":"ec5c3ce6ed1ca13a65df209f2e610a6c495bb9f28255c24666b10faa8444ac32","abstract_canon_sha256":"349c1b38caaeba84ee134ad3aac10cac106c11364d1d453a8cf706a5fa114315"},"schema_version":"1.0"},"canonical_sha256":"af55d6c5e06546e0d30a6d5dce6378bd54d173ae5bbd0a7a357d694f03116d66","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:09:12.055794Z","signature_b64":"w24UhD+zClUV1k6NFVBPv/X11mFOAomBeq2GYI+9oS1BF9QsSR3z68MVCnKfW2DTli64GCPwNznQoE7VJt03Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af55d6c5e06546e0d30a6d5dce6378bd54d173ae5bbd0a7a357d694f03116d66","last_reissued_at":"2026-05-18T03:09:12.055033Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:09:12.055033Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.12834","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":"2026-05-18T03:09:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iVhbLU0+fEouqD5+Xh8yXGeEbfKqhOvmMLt8HP/5ZAGyjXgtB0l/ENFtPiqbwBowe3Lxevx28A9apuSzd25SCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T04:42:32.571048Z"},"content_sha256":"417ae250bb1e83d841b93d97d26aacc80a046732199b98864623ffb07f0769dc","schema_version":"1.0","event_id":"sha256:417ae250bb1e83d841b93d97d26aacc80a046732199b98864623ffb07f0769dc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:V5K5NRPAMVDOBUYKNVO44Y3YXV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Underlying Stokes and de Rham structures for Arnold-type invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Hiroki Mizuno, Noboru Ito","submitted_at":"2026-05-13T00:04:50Z","abstract_excerpt":"We introduce a framework on dual complexes for studying Arnold-type invariants of immersed curves and immersed surfaces via local finite-difference structures associated with Alexander numberings. For generic immersed plane curves and generic immersed surfaces, we define locally normalized maps $d^k \\phi$ on dual skeleta and show that suitable evaluations recover the Arnold-type invariants $St_{(1)}$ and $St_{(2)}$. In particular, we establish normalized discrete Stokes-type compatibilities between adjacent dual skeleta and derive corresponding Shumakovitch-type identities for curves and surfa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.12834","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":"2026-05-18T03:09:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lXXqlS1SeBYdHrMERFD1Roc0cPaaYW7xq6jIswAcD1nJdrN1dLAzRXE4yHaV1aK4J7ML41ETRDlFDzzPJZNHDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T04:42:32.571662Z"},"content_sha256":"115890a623025bb55ee02e253773547923d597f3b07074bbf865badcb89c4f8e","schema_version":"1.0","event_id":"sha256:115890a623025bb55ee02e253773547923d597f3b07074bbf865badcb89c4f8e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V5K5NRPAMVDOBUYKNVO44Y3YXV/bundle.json","state_url":"https://pith.science/pith/V5K5NRPAMVDOBUYKNVO44Y3YXV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V5K5NRPAMVDOBUYKNVO44Y3YXV/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":"2026-06-11T04:42:32Z","links":{"resolver":"https://pith.science/pith/V5K5NRPAMVDOBUYKNVO44Y3YXV","bundle":"https://pith.science/pith/V5K5NRPAMVDOBUYKNVO44Y3YXV/bundle.json","state":"https://pith.science/pith/V5K5NRPAMVDOBUYKNVO44Y3YXV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V5K5NRPAMVDOBUYKNVO44Y3YXV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:V5K5NRPAMVDOBUYKNVO44Y3YXV","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":"349c1b38caaeba84ee134ad3aac10cac106c11364d1d453a8cf706a5fa114315","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-13T00:04:50Z","title_canon_sha256":"ec5c3ce6ed1ca13a65df209f2e610a6c495bb9f28255c24666b10faa8444ac32"},"schema_version":"1.0","source":{"id":"2605.12834","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.12834","created_at":"2026-05-18T03:09:12Z"},{"alias_kind":"arxiv_version","alias_value":"2605.12834v1","created_at":"2026-05-18T03:09:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.12834","created_at":"2026-05-18T03:09:12Z"},{"alias_kind":"pith_short_12","alias_value":"V5K5NRPAMVDO","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"V5K5NRPAMVDOBUYK","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"V5K5NRPA","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:115890a623025bb55ee02e253773547923d597f3b07074bbf865badcb89c4f8e","target":"graph","created_at":"2026-05-18T03:09:12Z","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 introduce a framework on dual complexes for studying Arnold-type invariants of immersed curves and immersed surfaces via local finite-difference structures associated with Alexander numberings. For generic immersed plane curves and generic immersed surfaces, we define locally normalized maps $d^k \\phi$ on dual skeleta and show that suitable evaluations recover the Arnold-type invariants $St_{(1)}$ and $St_{(2)}$. In particular, we establish normalized discrete Stokes-type compatibilities between adjacent dual skeleta and derive corresponding Shumakovitch-type identities for curves and surfa","authors_text":"Hiroki Mizuno, Noboru Ito","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-13T00:04:50Z","title":"Underlying Stokes and de Rham structures for Arnold-type invariants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.12834","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":"sha256:417ae250bb1e83d841b93d97d26aacc80a046732199b98864623ffb07f0769dc","target":"record","created_at":"2026-05-18T03:09:12Z","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":"349c1b38caaeba84ee134ad3aac10cac106c11364d1d453a8cf706a5fa114315","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-13T00:04:50Z","title_canon_sha256":"ec5c3ce6ed1ca13a65df209f2e610a6c495bb9f28255c24666b10faa8444ac32"},"schema_version":"1.0","source":{"id":"2605.12834","kind":"arxiv","version":1}},"canonical_sha256":"af55d6c5e06546e0d30a6d5dce6378bd54d173ae5bbd0a7a357d694f03116d66","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af55d6c5e06546e0d30a6d5dce6378bd54d173ae5bbd0a7a357d694f03116d66","first_computed_at":"2026-05-18T03:09:12.055033Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:09:12.055033Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w24UhD+zClUV1k6NFVBPv/X11mFOAomBeq2GYI+9oS1BF9QsSR3z68MVCnKfW2DTli64GCPwNznQoE7VJt03Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:09:12.055794Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.12834","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:417ae250bb1e83d841b93d97d26aacc80a046732199b98864623ffb07f0769dc","sha256:115890a623025bb55ee02e253773547923d597f3b07074bbf865badcb89c4f8e"],"state_sha256":"c5f013b40936b5fef93095dcbe3ea3366939a4a438e48705dac58149cf7b45fe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n2BL30+Ue9pWl9aOJSEtsK/Z5lL5t7OfGLpICe9KGMByqUGym8F3U12vIOsIBDgBnHaWZCfrsOvIru6mxydmBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T04:42:32.574902Z","bundle_sha256":"703eafc6f85fef688f1c525dec422056c436667b611d35f54dffc535ebf18f60"}}