{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:6AH37WENKNBSK75LHXUX572II7","short_pith_number":"pith:6AH37WEN","canonical_record":{"source":{"id":"1706.10206","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2017-06-30T14:00:53Z","cross_cats_sorted":["math.CO","math.NT"],"title_canon_sha256":"f207ec501f05b8d456f7a9e588fe5f7d77a6fca3932864a8c4b1096c8e9b4aa3","abstract_canon_sha256":"108fe92211f61388ee8e0f134928c5532c271551a86a65d16dabd212f4c6df17"},"schema_version":"1.0"},"canonical_sha256":"f00fbfd88d5343257fab3de97eff4847e96cf8cea6d1122fa7fe8b166b0492c8","source":{"kind":"arxiv","id":"1706.10206","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.10206","created_at":"2026-05-18T00:36:19Z"},{"alias_kind":"arxiv_version","alias_value":"1706.10206v3","created_at":"2026-05-18T00:36:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.10206","created_at":"2026-05-18T00:36:19Z"},{"alias_kind":"pith_short_12","alias_value":"6AH37WENKNBS","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6AH37WENKNBSK75L","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6AH37WEN","created_at":"2026-05-18T12:31:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:6AH37WENKNBSK75LHXUX572II7","target":"record","payload":{"canonical_record":{"source":{"id":"1706.10206","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2017-06-30T14:00:53Z","cross_cats_sorted":["math.CO","math.NT"],"title_canon_sha256":"f207ec501f05b8d456f7a9e588fe5f7d77a6fca3932864a8c4b1096c8e9b4aa3","abstract_canon_sha256":"108fe92211f61388ee8e0f134928c5532c271551a86a65d16dabd212f4c6df17"},"schema_version":"1.0"},"canonical_sha256":"f00fbfd88d5343257fab3de97eff4847e96cf8cea6d1122fa7fe8b166b0492c8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:19.094101Z","signature_b64":"BKrdrn50oaNAVMPIDAqaaWS10MS2YQWUJg1l5iCPQUZemSyPX7RgpHevu6DGrQ7dwIRyDY60OKnQlrDJ8ocXAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f00fbfd88d5343257fab3de97eff4847e96cf8cea6d1122fa7fe8b166b0492c8","last_reissued_at":"2026-05-18T00:36:19.093486Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:19.093486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.10206","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:36:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fU3VGEtAzuwZBP8Z4h4ZXapR1NFdXEzDRamczh5vfe5/GxNOJpq8h5EQ2900YigqG0i8gRVA1XURInzzDm2oDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T09:32:31.832006Z"},"content_sha256":"595485179a8bcfb7babaf1e8c4aa56b54dde740ee6064d1bba4fc1aedfe68df3","schema_version":"1.0","event_id":"sha256:595485179a8bcfb7babaf1e8c4aa56b54dde740ee6064d1bba4fc1aedfe68df3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:6AH37WENKNBSK75LHXUX572II7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sums of Palindromes: an Approach via Automata","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.NT"],"primary_cat":"cs.FL","authors_text":"Aayush Rajasekaran, Jeffrey Shallit, Tim Smith","submitted_at":"2017-06-30T14:00:53Z","abstract_excerpt":"Recently, Cilleruelo, Luca, & Baxter proved, for all bases b >= 5, that every natural number is the sum of at most 3 natural numbers whose base-b representation is a palindrome. However, the cases b = 2, 3, 4 were left unresolved.\n  We prove, using a decision procedure based on automata, that every natural number is the sum of at most 4 natural numbers whose base-2 representation is a palindrome. Here the constant 4 is optimal. We obtain similar results for bases 3 and 4, thus completely resolving the problem.\n  We consider some other variations on this problem, and prove similar results. We a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.10206","kind":"arxiv","version":3},"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":"2026-05-18T00:36:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MqRoJwWscBy8r6Xp1vPFtcAqtp+xo1gNSSwAihF7Eseze1/Rruz/5X8RPGUfHQBJ200OOgtTEWRalu0U23IIDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T09:32:31.832399Z"},"content_sha256":"92eee46705c6b4ff4188d820beb6f1157e86fd9e5848e6628131c88705885fc8","schema_version":"1.0","event_id":"sha256:92eee46705c6b4ff4188d820beb6f1157e86fd9e5848e6628131c88705885fc8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6AH37WENKNBSK75LHXUX572II7/bundle.json","state_url":"https://pith.science/pith/6AH37WENKNBSK75LHXUX572II7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6AH37WENKNBSK75LHXUX572II7/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":"2026-05-30T09:32:31Z","links":{"resolver":"https://pith.science/pith/6AH37WENKNBSK75LHXUX572II7","bundle":"https://pith.science/pith/6AH37WENKNBSK75LHXUX572II7/bundle.json","state":"https://pith.science/pith/6AH37WENKNBSK75LHXUX572II7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6AH37WENKNBSK75LHXUX572II7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:6AH37WENKNBSK75LHXUX572II7","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":"108fe92211f61388ee8e0f134928c5532c271551a86a65d16dabd212f4c6df17","cross_cats_sorted":["math.CO","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2017-06-30T14:00:53Z","title_canon_sha256":"f207ec501f05b8d456f7a9e588fe5f7d77a6fca3932864a8c4b1096c8e9b4aa3"},"schema_version":"1.0","source":{"id":"1706.10206","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.10206","created_at":"2026-05-18T00:36:19Z"},{"alias_kind":"arxiv_version","alias_value":"1706.10206v3","created_at":"2026-05-18T00:36:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.10206","created_at":"2026-05-18T00:36:19Z"},{"alias_kind":"pith_short_12","alias_value":"6AH37WENKNBS","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6AH37WENKNBSK75L","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6AH37WEN","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:92eee46705c6b4ff4188d820beb6f1157e86fd9e5848e6628131c88705885fc8","target":"graph","created_at":"2026-05-18T00:36:19Z","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":"Recently, Cilleruelo, Luca, & Baxter proved, for all bases b >= 5, that every natural number is the sum of at most 3 natural numbers whose base-b representation is a palindrome. However, the cases b = 2, 3, 4 were left unresolved.\n  We prove, using a decision procedure based on automata, that every natural number is the sum of at most 4 natural numbers whose base-2 representation is a palindrome. Here the constant 4 is optimal. We obtain similar results for bases 3 and 4, thus completely resolving the problem.\n  We consider some other variations on this problem, and prove similar results. We a","authors_text":"Aayush Rajasekaran, Jeffrey Shallit, Tim Smith","cross_cats":["math.CO","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2017-06-30T14:00:53Z","title":"Sums of Palindromes: an Approach via Automata"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.10206","kind":"arxiv","version":3},"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":"sha256:595485179a8bcfb7babaf1e8c4aa56b54dde740ee6064d1bba4fc1aedfe68df3","target":"record","created_at":"2026-05-18T00:36:19Z","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":"108fe92211f61388ee8e0f134928c5532c271551a86a65d16dabd212f4c6df17","cross_cats_sorted":["math.CO","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2017-06-30T14:00:53Z","title_canon_sha256":"f207ec501f05b8d456f7a9e588fe5f7d77a6fca3932864a8c4b1096c8e9b4aa3"},"schema_version":"1.0","source":{"id":"1706.10206","kind":"arxiv","version":3}},"canonical_sha256":"f00fbfd88d5343257fab3de97eff4847e96cf8cea6d1122fa7fe8b166b0492c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f00fbfd88d5343257fab3de97eff4847e96cf8cea6d1122fa7fe8b166b0492c8","first_computed_at":"2026-05-18T00:36:19.093486Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:19.093486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BKrdrn50oaNAVMPIDAqaaWS10MS2YQWUJg1l5iCPQUZemSyPX7RgpHevu6DGrQ7dwIRyDY60OKnQlrDJ8ocXAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:19.094101Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.10206","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:595485179a8bcfb7babaf1e8c4aa56b54dde740ee6064d1bba4fc1aedfe68df3","sha256:92eee46705c6b4ff4188d820beb6f1157e86fd9e5848e6628131c88705885fc8"],"state_sha256":"3027b28f91ab24031f66f8c29314898ccea3b924866ef2a0647e021d4f4a93f9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2oad+QNpaBgoKSsZYcbD99OtoSdm+b8n9uRANmeOiQvtK9Ci9l6cqdlQMa7xbLyC7cfgTIM8uHLJmbr8yq93Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T09:32:31.835171Z","bundle_sha256":"99b4b6e244aae35ad5d459b424ee8f57b13e5d884e78f8cebe50150c4adfa73a"}}