{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:MBT2ROXDDZEPALPQB4QBMR5Z5U","short_pith_number":"pith:MBT2ROXD","canonical_record":{"source":{"id":"2603.10334","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-03-11T02:06:10Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"4eec6cd29fcf45d63d90300cd4dfd9709773d5c36e58087e6fc1db3d29c8dc29","abstract_canon_sha256":"423aeeca05b6ee0e559e4cca6d39c95b0585e0a6e5c29df1e4baf06e4b2fe039"},"schema_version":"1.0"},"canonical_sha256":"6067a8bae31e48f02df00f201647b9ed27f21db05f60c7f796b18b89a32c2eb9","source":{"kind":"arxiv","id":"2603.10334","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.10334","created_at":"2026-05-20T00:04:27Z"},{"alias_kind":"arxiv_version","alias_value":"2603.10334v2","created_at":"2026-05-20T00:04:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.10334","created_at":"2026-05-20T00:04:27Z"},{"alias_kind":"pith_short_12","alias_value":"MBT2ROXDDZEP","created_at":"2026-05-20T00:04:27Z"},{"alias_kind":"pith_short_16","alias_value":"MBT2ROXDDZEPALPQ","created_at":"2026-05-20T00:04:27Z"},{"alias_kind":"pith_short_8","alias_value":"MBT2ROXD","created_at":"2026-05-20T00:04:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:MBT2ROXDDZEPALPQB4QBMR5Z5U","target":"record","payload":{"canonical_record":{"source":{"id":"2603.10334","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-03-11T02:06:10Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"4eec6cd29fcf45d63d90300cd4dfd9709773d5c36e58087e6fc1db3d29c8dc29","abstract_canon_sha256":"423aeeca05b6ee0e559e4cca6d39c95b0585e0a6e5c29df1e4baf06e4b2fe039"},"schema_version":"1.0"},"canonical_sha256":"6067a8bae31e48f02df00f201647b9ed27f21db05f60c7f796b18b89a32c2eb9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:04:27.873945Z","signature_b64":"LJ68becppiIyh6u2y0pdep3JXj/nJ2wi0yVEj69t1ie8CprP8UR/PN4AwftrEGuNtK2cfVMQNE2BAjT7jtbiAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6067a8bae31e48f02df00f201647b9ed27f21db05f60c7f796b18b89a32c2eb9","last_reissued_at":"2026-05-20T00:04:27.873015Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:04:27.873015Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2603.10334","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":"2026-05-20T00:04:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lRE0yow/M6VauIfaYY3yL4RnJZe0d5Tt/2CBhNvV1HvONbEDFVfy0zpMZluuVXCrAo1u8tCZTGaWpZQEq8WGAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T18:07:04.154438Z"},"content_sha256":"a4a34befc67e75d16748aa981ca67f6ebdfd0a8c4b006493b6d2ec37bf3fe737","schema_version":"1.0","event_id":"sha256:a4a34befc67e75d16748aa981ca67f6ebdfd0a8c4b006493b6d2ec37bf3fe737"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:MBT2ROXDDZEPALPQB4QBMR5Z5U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral Bounds for Antipodal Graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CO","authors_text":"Samuel Korsky","submitted_at":"2026-03-11T02:06:10Z","abstract_excerpt":"Suppose $\\left\\{x_1, \\dots, x_n\\right\\} \\subset \\mathbb{R}^2$ is a set of $n$ points in the plane with diameter $\\leq 1$, meaning $|x_i - x_j| \\leq 1$ for all $1 \\leq i,j \\leq n$. We show that the ratio of the number of ``neighbors'' (ordered pairs of points with distance $\\leq \\varepsilon$) to the number of ``antipodes'' (ordered pairs of points with distance $\\geq 1 - \\varepsilon$) is $\\gtrsim\\varepsilon^{1/2 + o(1)}$, attaining the conjectured correct asymptotic within a polylog factor and improving the $\\gtrsim\\varepsilon^{3/4+o(1)}$ bound of Steinerberger (2025). In dimensions $d\\ge3$ we "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.10334","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/2603.10334/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":"2026-05-20T00:04:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vPEFjYuwLVSvwTodeSvbWyd2G+eqs3Uel6JUoEvQP3P/MvfVDqLlNauu3/FfpfWJYO+Cp2+F9WH3V8QoELNcAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T18:07:04.154819Z"},"content_sha256":"bd440bce5862e860f8ec121ca44ad1d0707c0346c2bcea193327a1e87ff89914","schema_version":"1.0","event_id":"sha256:bd440bce5862e860f8ec121ca44ad1d0707c0346c2bcea193327a1e87ff89914"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MBT2ROXDDZEPALPQB4QBMR5Z5U/bundle.json","state_url":"https://pith.science/pith/MBT2ROXDDZEPALPQB4QBMR5Z5U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MBT2ROXDDZEPALPQB4QBMR5Z5U/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":"2026-06-10T18:07:04Z","links":{"resolver":"https://pith.science/pith/MBT2ROXDDZEPALPQB4QBMR5Z5U","bundle":"https://pith.science/pith/MBT2ROXDDZEPALPQB4QBMR5Z5U/bundle.json","state":"https://pith.science/pith/MBT2ROXDDZEPALPQB4QBMR5Z5U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MBT2ROXDDZEPALPQB4QBMR5Z5U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:MBT2ROXDDZEPALPQB4QBMR5Z5U","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":"423aeeca05b6ee0e559e4cca6d39c95b0585e0a6e5c29df1e4baf06e4b2fe039","cross_cats_sorted":["math.MG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-03-11T02:06:10Z","title_canon_sha256":"4eec6cd29fcf45d63d90300cd4dfd9709773d5c36e58087e6fc1db3d29c8dc29"},"schema_version":"1.0","source":{"id":"2603.10334","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.10334","created_at":"2026-05-20T00:04:27Z"},{"alias_kind":"arxiv_version","alias_value":"2603.10334v2","created_at":"2026-05-20T00:04:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.10334","created_at":"2026-05-20T00:04:27Z"},{"alias_kind":"pith_short_12","alias_value":"MBT2ROXDDZEP","created_at":"2026-05-20T00:04:27Z"},{"alias_kind":"pith_short_16","alias_value":"MBT2ROXDDZEPALPQ","created_at":"2026-05-20T00:04:27Z"},{"alias_kind":"pith_short_8","alias_value":"MBT2ROXD","created_at":"2026-05-20T00:04:27Z"}],"graph_snapshots":[{"event_id":"sha256:bd440bce5862e860f8ec121ca44ad1d0707c0346c2bcea193327a1e87ff89914","target":"graph","created_at":"2026-05-20T00:04:27Z","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/2603.10334/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Suppose $\\left\\{x_1, \\dots, x_n\\right\\} \\subset \\mathbb{R}^2$ is a set of $n$ points in the plane with diameter $\\leq 1$, meaning $|x_i - x_j| \\leq 1$ for all $1 \\leq i,j \\leq n$. We show that the ratio of the number of ``neighbors'' (ordered pairs of points with distance $\\leq \\varepsilon$) to the number of ``antipodes'' (ordered pairs of points with distance $\\geq 1 - \\varepsilon$) is $\\gtrsim\\varepsilon^{1/2 + o(1)}$, attaining the conjectured correct asymptotic within a polylog factor and improving the $\\gtrsim\\varepsilon^{3/4+o(1)}$ bound of Steinerberger (2025). In dimensions $d\\ge3$ we ","authors_text":"Samuel Korsky","cross_cats":["math.MG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-03-11T02:06:10Z","title":"Spectral Bounds for Antipodal Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.10334","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:a4a34befc67e75d16748aa981ca67f6ebdfd0a8c4b006493b6d2ec37bf3fe737","target":"record","created_at":"2026-05-20T00:04:27Z","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":"423aeeca05b6ee0e559e4cca6d39c95b0585e0a6e5c29df1e4baf06e4b2fe039","cross_cats_sorted":["math.MG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-03-11T02:06:10Z","title_canon_sha256":"4eec6cd29fcf45d63d90300cd4dfd9709773d5c36e58087e6fc1db3d29c8dc29"},"schema_version":"1.0","source":{"id":"2603.10334","kind":"arxiv","version":2}},"canonical_sha256":"6067a8bae31e48f02df00f201647b9ed27f21db05f60c7f796b18b89a32c2eb9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6067a8bae31e48f02df00f201647b9ed27f21db05f60c7f796b18b89a32c2eb9","first_computed_at":"2026-05-20T00:04:27.873015Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:04:27.873015Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LJ68becppiIyh6u2y0pdep3JXj/nJ2wi0yVEj69t1ie8CprP8UR/PN4AwftrEGuNtK2cfVMQNE2BAjT7jtbiAA==","signature_status":"signed_v1","signed_at":"2026-05-20T00:04:27.873945Z","signed_message":"canonical_sha256_bytes"},"source_id":"2603.10334","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4a34befc67e75d16748aa981ca67f6ebdfd0a8c4b006493b6d2ec37bf3fe737","sha256:bd440bce5862e860f8ec121ca44ad1d0707c0346c2bcea193327a1e87ff89914"],"state_sha256":"e3daa4568420a5dd3ecddee7cc465b37ecdb7a8e3f03c3e47e1960fab92660d9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DEj1w11k5tPtVqVbGk2vyfDxJwhcB2J715PeVbYaBAKIFGI9nq2vzxE1EBNCKiVi71VQjQiBDwWSIfoK0DJcCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T18:07:04.156821Z","bundle_sha256":"43e09a53a8808814e8f05092c0e8558f92b06363b4381eaa1f7ff107112777ec"}}