{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:RMWNC3G3SBENAZLPPMDWGDA3L7","short_pith_number":"pith:RMWNC3G3","canonical_record":{"source":{"id":"2405.05267","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.HO","submitted_at":"2024-04-24T20:10:37Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"6b604c56b567ad2aa5e5ad7066653afb034b305fb660d7f4f370230de1c4a09b","abstract_canon_sha256":"87033819b837ba746d3524ff2ffdc763d7e5aff2be516fb4c704859a572239b1"},"schema_version":"1.0"},"canonical_sha256":"8b2cd16cdb9048d0656f7b07630c1b5fe95eb59460bfb03fa4092d99f73995c6","source":{"kind":"arxiv","id":"2405.05267","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.05267","created_at":"2026-07-05T08:17:15Z"},{"alias_kind":"arxiv_version","alias_value":"2405.05267v1","created_at":"2026-07-05T08:17:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.05267","created_at":"2026-07-05T08:17:15Z"},{"alias_kind":"pith_short_12","alias_value":"RMWNC3G3SBEN","created_at":"2026-07-05T08:17:15Z"},{"alias_kind":"pith_short_16","alias_value":"RMWNC3G3SBENAZLP","created_at":"2026-07-05T08:17:15Z"},{"alias_kind":"pith_short_8","alias_value":"RMWNC3G3","created_at":"2026-07-05T08:17:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:RMWNC3G3SBENAZLPPMDWGDA3L7","target":"record","payload":{"canonical_record":{"source":{"id":"2405.05267","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.HO","submitted_at":"2024-04-24T20:10:37Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"6b604c56b567ad2aa5e5ad7066653afb034b305fb660d7f4f370230de1c4a09b","abstract_canon_sha256":"87033819b837ba746d3524ff2ffdc763d7e5aff2be516fb4c704859a572239b1"},"schema_version":"1.0"},"canonical_sha256":"8b2cd16cdb9048d0656f7b07630c1b5fe95eb59460bfb03fa4092d99f73995c6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:17:15.933500Z","signature_b64":"owkH+2qD6W5SFQBVDDPvhhgd94tt1YCplv8Q2YkgTlTVaGQMU5s3uvLKyeXdBf5YcEvtvvEPedh3BorRc4RHDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8b2cd16cdb9048d0656f7b07630c1b5fe95eb59460bfb03fa4092d99f73995c6","last_reissued_at":"2026-07-05T08:17:15.933033Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:17:15.933033Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2405.05267","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":"2026-07-05T08:17:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K8FSK+HKIDvefIdEEhPalTpyzxroXXPQU1pOJZ6cKtiorkcWdPicH2baK1Y6OKTc7+feG9aFMT2CQTuKYGVrAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T18:26:47.352162Z"},"content_sha256":"df9e23bf3dfd7d5b52225690fbcdfe718a1fbff3a5dc94ea5a9e57bd3c75c60d","schema_version":"1.0","event_id":"sha256:df9e23bf3dfd7d5b52225690fbcdfe718a1fbff3a5dc94ea5a9e57bd3c75c60d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:RMWNC3G3SBENAZLPPMDWGDA3L7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$v$-Palindromes: An Analogy to the Palindromes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.HO","authors_text":"Chris Bispels, Daniel Tsai, Eliel Sosis, Muhammet Boran, Steven J. Miller","submitted_at":"2024-04-24T20:10:37Z","abstract_excerpt":"Around the year 2007, one of the authors, Tsai, accidentally discovered a property of the number $198$ he saw on the license plate of a car. Namely, if we take $198$ and its reversal $891$, which have prime factorizations $198 = 2\\cdot 3^2\\cdot 11$ and $891 = 3^4\\cdot 11$ respectively, and sum the numbers appearing in each factorization getting $2+3+2+11 = 18$ and $3+4+11 = 18$, both sums are $18$. Such numbers were later named $v$-palindromes because they can be viewed as an analogy to the usual palindromes. In this article, we introduce the concept of a $v$-palindrome in base $b$ and prove t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.05267","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/2405.05267/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":"2026-07-05T08:17:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y+4ju5zO5S3d/uyeKB7QN9Tu14WKaVtQpIFZR9oAlO7ESwwIfJ8t6e52B2Wbg9RzVFJq1V2M1MM6sjqZL8xHAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T18:26:47.352553Z"},"content_sha256":"1b59ee3432cae7175856ad95300c23e01ac1b9c68969ca759ab461b95dd9bbab","schema_version":"1.0","event_id":"sha256:1b59ee3432cae7175856ad95300c23e01ac1b9c68969ca759ab461b95dd9bbab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RMWNC3G3SBENAZLPPMDWGDA3L7/bundle.json","state_url":"https://pith.science/pith/RMWNC3G3SBENAZLPPMDWGDA3L7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RMWNC3G3SBENAZLPPMDWGDA3L7/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":"2026-07-06T18:26:47Z","links":{"resolver":"https://pith.science/pith/RMWNC3G3SBENAZLPPMDWGDA3L7","bundle":"https://pith.science/pith/RMWNC3G3SBENAZLPPMDWGDA3L7/bundle.json","state":"https://pith.science/pith/RMWNC3G3SBENAZLPPMDWGDA3L7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RMWNC3G3SBENAZLPPMDWGDA3L7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:RMWNC3G3SBENAZLPPMDWGDA3L7","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":"87033819b837ba746d3524ff2ffdc763d7e5aff2be516fb4c704859a572239b1","cross_cats_sorted":["math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.HO","submitted_at":"2024-04-24T20:10:37Z","title_canon_sha256":"6b604c56b567ad2aa5e5ad7066653afb034b305fb660d7f4f370230de1c4a09b"},"schema_version":"1.0","source":{"id":"2405.05267","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.05267","created_at":"2026-07-05T08:17:15Z"},{"alias_kind":"arxiv_version","alias_value":"2405.05267v1","created_at":"2026-07-05T08:17:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.05267","created_at":"2026-07-05T08:17:15Z"},{"alias_kind":"pith_short_12","alias_value":"RMWNC3G3SBEN","created_at":"2026-07-05T08:17:15Z"},{"alias_kind":"pith_short_16","alias_value":"RMWNC3G3SBENAZLP","created_at":"2026-07-05T08:17:15Z"},{"alias_kind":"pith_short_8","alias_value":"RMWNC3G3","created_at":"2026-07-05T08:17:15Z"}],"graph_snapshots":[{"event_id":"sha256:1b59ee3432cae7175856ad95300c23e01ac1b9c68969ca759ab461b95dd9bbab","target":"graph","created_at":"2026-07-05T08:17:15Z","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/2405.05267/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Around the year 2007, one of the authors, Tsai, accidentally discovered a property of the number $198$ he saw on the license plate of a car. Namely, if we take $198$ and its reversal $891$, which have prime factorizations $198 = 2\\cdot 3^2\\cdot 11$ and $891 = 3^4\\cdot 11$ respectively, and sum the numbers appearing in each factorization getting $2+3+2+11 = 18$ and $3+4+11 = 18$, both sums are $18$. Such numbers were later named $v$-palindromes because they can be viewed as an analogy to the usual palindromes. In this article, we introduce the concept of a $v$-palindrome in base $b$ and prove t","authors_text":"Chris Bispels, Daniel Tsai, Eliel Sosis, Muhammet Boran, Steven J. Miller","cross_cats":["math.NT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.HO","submitted_at":"2024-04-24T20:10:37Z","title":"$v$-Palindromes: An Analogy to the Palindromes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.05267","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:df9e23bf3dfd7d5b52225690fbcdfe718a1fbff3a5dc94ea5a9e57bd3c75c60d","target":"record","created_at":"2026-07-05T08:17:15Z","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":"87033819b837ba746d3524ff2ffdc763d7e5aff2be516fb4c704859a572239b1","cross_cats_sorted":["math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.HO","submitted_at":"2024-04-24T20:10:37Z","title_canon_sha256":"6b604c56b567ad2aa5e5ad7066653afb034b305fb660d7f4f370230de1c4a09b"},"schema_version":"1.0","source":{"id":"2405.05267","kind":"arxiv","version":1}},"canonical_sha256":"8b2cd16cdb9048d0656f7b07630c1b5fe95eb59460bfb03fa4092d99f73995c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8b2cd16cdb9048d0656f7b07630c1b5fe95eb59460bfb03fa4092d99f73995c6","first_computed_at":"2026-07-05T08:17:15.933033Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:17:15.933033Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"owkH+2qD6W5SFQBVDDPvhhgd94tt1YCplv8Q2YkgTlTVaGQMU5s3uvLKyeXdBf5YcEvtvvEPedh3BorRc4RHDg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:17:15.933500Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.05267","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:df9e23bf3dfd7d5b52225690fbcdfe718a1fbff3a5dc94ea5a9e57bd3c75c60d","sha256:1b59ee3432cae7175856ad95300c23e01ac1b9c68969ca759ab461b95dd9bbab"],"state_sha256":"dc3a3ce6bcb0cde2e5343bbf5abfefc6d493acc1597f3b5aa4375a9bf658a1d4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dR1DrsNzX3uEDWkTSqbeXI4C3QZZXVznq5srdK073/sU6XN5NHDP3alv5qg5+bNFvyNFL28sXwyihx/QS0RZBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T18:26:47.354936Z","bundle_sha256":"8673e5ebfd28849c943dbdf34be60cb7b891e174c8aefa891a9102ba88069984"}}