{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:U2NDVURHIIJS555XYQQXA76TT2","short_pith_number":"pith:U2NDVURH","canonical_record":{"source":{"id":"2605.18994","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-18T18:12:43Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"fd4e420bedbd428d9d6a4157a83e7a0797c4ef47bc0e6541b204406b63de12c3","abstract_canon_sha256":"8e2ec344a986e815f2b1e3662afd5f7673eba6a7e85c14da712d7bccb798f090"},"schema_version":"1.0"},"canonical_sha256":"a69a3ad22742132ef7b7c421707fd39eab4011bdf937fddd7282ee8344990a29","source":{"kind":"arxiv","id":"2605.18994","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.18994","created_at":"2026-05-20T00:06:42Z"},{"alias_kind":"arxiv_version","alias_value":"2605.18994v1","created_at":"2026-05-20T00:06:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.18994","created_at":"2026-05-20T00:06:42Z"},{"alias_kind":"pith_short_12","alias_value":"U2NDVURHIIJS","created_at":"2026-05-20T00:06:42Z"},{"alias_kind":"pith_short_16","alias_value":"U2NDVURHIIJS555X","created_at":"2026-05-20T00:06:42Z"},{"alias_kind":"pith_short_8","alias_value":"U2NDVURH","created_at":"2026-05-20T00:06:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:U2NDVURHIIJS555XYQQXA76TT2","target":"record","payload":{"canonical_record":{"source":{"id":"2605.18994","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-18T18:12:43Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"fd4e420bedbd428d9d6a4157a83e7a0797c4ef47bc0e6541b204406b63de12c3","abstract_canon_sha256":"8e2ec344a986e815f2b1e3662afd5f7673eba6a7e85c14da712d7bccb798f090"},"schema_version":"1.0"},"canonical_sha256":"a69a3ad22742132ef7b7c421707fd39eab4011bdf937fddd7282ee8344990a29","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:06:42.020299Z","signature_b64":"Y/NrgFfkQyxvHmPU49/vUg3OSJdEIYxCFuxdhzPFeL681KuNrzmAS7OeWYZNeBu6vlem7qYrO+aO6df3wmkEDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a69a3ad22742132ef7b7c421707fd39eab4011bdf937fddd7282ee8344990a29","last_reissued_at":"2026-05-20T00:06:42.019596Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:06:42.019596Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.18994","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":"2026-05-20T00:06:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U5uq2t06mlO26mKbzj1t1uxMD0sIC20TObUPOsq3wgZKw84bxvJEhe3+YdGtGzcl9SVFIXifV9S4gqnUp0+vBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T11:50:39.048241Z"},"content_sha256":"88837e91912bfc5cf5bbf0c653f831c5fc17b13be155973fe73b4a73e7ceecb8","schema_version":"1.0","event_id":"sha256:88837e91912bfc5cf5bbf0c653f831c5fc17b13be155973fe73b4a73e7ceecb8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:U2NDVURHIIJS555XYQQXA76TT2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Planar multilinks and rational singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.GT","authors_text":"M\\'arton Beke, Olga Plamenevskaya","submitted_at":"2026-05-18T18:12:43Z","abstract_excerpt":"Fibered multilinks are a generalization of classical fibered knots and open books that arise in the study of surface singularities and Milnor fibrations. We prove that if the canonical contact structure on the link of a surface singularity is supported by a planar multilink open book, then the singularity must be rational, and that sandwiched singularities are characterized by admitting planar multilinks with a component of multiplicity 1. We also show that some topological properties of planar open books extend to planar multilinks: symplectic fillings are negative definite and cannot contain"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18994","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/2605.18994/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":"2026-05-20T00:06:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YwEIsQnCxwELBqnPFUcfaJ9oP6YXJj8z+dLyR25x/AcJJcRvceHCzWbi4j4ZZpfh+5Hyp0TOsAUeLPo8P/PQDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T11:50:39.048636Z"},"content_sha256":"ff195240d801434ff769e4fed4c1e6f908a0ac1f63e9b681259884afc9f2b41c","schema_version":"1.0","event_id":"sha256:ff195240d801434ff769e4fed4c1e6f908a0ac1f63e9b681259884afc9f2b41c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U2NDVURHIIJS555XYQQXA76TT2/bundle.json","state_url":"https://pith.science/pith/U2NDVURHIIJS555XYQQXA76TT2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U2NDVURHIIJS555XYQQXA76TT2/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":"2026-05-28T11:50:39Z","links":{"resolver":"https://pith.science/pith/U2NDVURHIIJS555XYQQXA76TT2","bundle":"https://pith.science/pith/U2NDVURHIIJS555XYQQXA76TT2/bundle.json","state":"https://pith.science/pith/U2NDVURHIIJS555XYQQXA76TT2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U2NDVURHIIJS555XYQQXA76TT2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:U2NDVURHIIJS555XYQQXA76TT2","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":"8e2ec344a986e815f2b1e3662afd5f7673eba6a7e85c14da712d7bccb798f090","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-18T18:12:43Z","title_canon_sha256":"fd4e420bedbd428d9d6a4157a83e7a0797c4ef47bc0e6541b204406b63de12c3"},"schema_version":"1.0","source":{"id":"2605.18994","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.18994","created_at":"2026-05-20T00:06:42Z"},{"alias_kind":"arxiv_version","alias_value":"2605.18994v1","created_at":"2026-05-20T00:06:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.18994","created_at":"2026-05-20T00:06:42Z"},{"alias_kind":"pith_short_12","alias_value":"U2NDVURHIIJS","created_at":"2026-05-20T00:06:42Z"},{"alias_kind":"pith_short_16","alias_value":"U2NDVURHIIJS555X","created_at":"2026-05-20T00:06:42Z"},{"alias_kind":"pith_short_8","alias_value":"U2NDVURH","created_at":"2026-05-20T00:06:42Z"}],"graph_snapshots":[{"event_id":"sha256:ff195240d801434ff769e4fed4c1e6f908a0ac1f63e9b681259884afc9f2b41c","target":"graph","created_at":"2026-05-20T00:06:42Z","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/2605.18994/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Fibered multilinks are a generalization of classical fibered knots and open books that arise in the study of surface singularities and Milnor fibrations. We prove that if the canonical contact structure on the link of a surface singularity is supported by a planar multilink open book, then the singularity must be rational, and that sandwiched singularities are characterized by admitting planar multilinks with a component of multiplicity 1. We also show that some topological properties of planar open books extend to planar multilinks: symplectic fillings are negative definite and cannot contain","authors_text":"M\\'arton Beke, Olga Plamenevskaya","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-18T18:12:43Z","title":"Planar multilinks and rational singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18994","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":"sha256:88837e91912bfc5cf5bbf0c653f831c5fc17b13be155973fe73b4a73e7ceecb8","target":"record","created_at":"2026-05-20T00:06:42Z","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":"8e2ec344a986e815f2b1e3662afd5f7673eba6a7e85c14da712d7bccb798f090","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-18T18:12:43Z","title_canon_sha256":"fd4e420bedbd428d9d6a4157a83e7a0797c4ef47bc0e6541b204406b63de12c3"},"schema_version":"1.0","source":{"id":"2605.18994","kind":"arxiv","version":1}},"canonical_sha256":"a69a3ad22742132ef7b7c421707fd39eab4011bdf937fddd7282ee8344990a29","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a69a3ad22742132ef7b7c421707fd39eab4011bdf937fddd7282ee8344990a29","first_computed_at":"2026-05-20T00:06:42.019596Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:06:42.019596Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y/NrgFfkQyxvHmPU49/vUg3OSJdEIYxCFuxdhzPFeL681KuNrzmAS7OeWYZNeBu6vlem7qYrO+aO6df3wmkEDA==","signature_status":"signed_v1","signed_at":"2026-05-20T00:06:42.020299Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.18994","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88837e91912bfc5cf5bbf0c653f831c5fc17b13be155973fe73b4a73e7ceecb8","sha256:ff195240d801434ff769e4fed4c1e6f908a0ac1f63e9b681259884afc9f2b41c"],"state_sha256":"00594d1c44e093ee8a1a34cf9ea33715326a13db9678190cfb21d5c6f64da67e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fahmjruE1iPXyyz8eGfi6dTM9OQeMIIqTTNH2yaQfIaiscRLAc4Li59oy3BB/XKO6A7Ojblz3J9ON9Hh0jxKAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T11:50:39.050750Z","bundle_sha256":"4095a751f7774b8903bd56b20a7299a23c7fa121f4e4dfbae6cc4aad1551c6f0"}}