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We observed mid-transit times of each of the inner two planets with the Astrophysical Research Consortium (ARC) 3.5 m Telescope at Apache Point Observatory (APO) to help constrain the planet masses with transit timing variations, and we outline a procedure for analyzing transit observations of late-M stars with APO. The transit times of TRAPPIST-1 b and c are $\\mathrm{BJD}_{\\mathrm{TDB}} = 2457580.87634^{+0.00034}_{-0.00034}$ and $2457558.89477^{+0.00080}_{-0.00085}$, respectively, which will help constrain the planet masses."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1801.04460","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2018-01-13T16:14:25Z","cross_cats_sorted":[],"title_canon_sha256":"8a949c96cbb3b584f327bdc40d859aa16927974c624f99867d6c9b3538ac94fc","abstract_canon_sha256":"791016d6cf35fb8b0cefa6c63ff7683ebd47272f91349343b9c61e621b4b5fc4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:06.423148Z","signature_b64":"SQkxPZRQwwO9oMwsToAODmds7PkeMljy/qRV0spXahd/k6FYIo7J4yx+ovpFdb3bUZCbpFQNCkeGy0sTMDEDCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8200d755596d99beda3452161ca51d298a1b05ca476c6b407e39729ebb030b86","last_reissued_at":"2026-05-18T00:26:06.422649Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:06.422649Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Photometric Analysis and Transit Times of TRAPPIST-1 b and c","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.EP","authors_text":"Brett M. 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