{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:QJPVO33YU24PFCGRN2V2LVPBOB","short_pith_number":"pith:QJPVO33Y","canonical_record":{"source":{"id":"1903.01074","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2019-03-04T05:14:32Z","cross_cats_sorted":[],"title_canon_sha256":"8a9462c248a4c62d298297b082276d2a442d48355e2a24175a617b053d8a771a","abstract_canon_sha256":"ba9dd8b2bb0b8591f009eabb41fc91319a9895e21649e42514486e536020376b"},"schema_version":"1.0"},"canonical_sha256":"825f576f78a6b8f288d16eaba5d5e1707a83ce3b4d1c2f00bff7261a4dbc3ad8","source":{"kind":"arxiv","id":"1903.01074","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.01074","created_at":"2026-05-17T23:52:12Z"},{"alias_kind":"arxiv_version","alias_value":"1903.01074v1","created_at":"2026-05-17T23:52:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.01074","created_at":"2026-05-17T23:52:12Z"},{"alias_kind":"pith_short_12","alias_value":"QJPVO33YU24P","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"QJPVO33YU24PFCGR","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"QJPVO33Y","created_at":"2026-05-18T12:33:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:QJPVO33YU24PFCGRN2V2LVPBOB","target":"record","payload":{"canonical_record":{"source":{"id":"1903.01074","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2019-03-04T05:14:32Z","cross_cats_sorted":[],"title_canon_sha256":"8a9462c248a4c62d298297b082276d2a442d48355e2a24175a617b053d8a771a","abstract_canon_sha256":"ba9dd8b2bb0b8591f009eabb41fc91319a9895e21649e42514486e536020376b"},"schema_version":"1.0"},"canonical_sha256":"825f576f78a6b8f288d16eaba5d5e1707a83ce3b4d1c2f00bff7261a4dbc3ad8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:12.387928Z","signature_b64":"RXtBy2Nxtd1uZXhKwo+eWVdE0EUXKlkvLQrakDpbup4z7GoRJHzw/S3b4GKL/clA9EU9y3wvOQjp4kdp/rolAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"825f576f78a6b8f288d16eaba5d5e1707a83ce3b4d1c2f00bff7261a4dbc3ad8","last_reissued_at":"2026-05-17T23:52:12.387250Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:12.387250Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.01074","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":"2026-05-17T23:52:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U8sCfoC2DfpsljFdlArQSffQzDwU2iqKL5UBB1/0lufqVOTNq6JOSMEqAUDh3JLIazzZ23w2FdTtVpd4uZHwCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:33:15.817869Z"},"content_sha256":"1d5459390ccd4f5e4b5a0dc3d4bf4669c00217828e7348f8007b8affb1752625","schema_version":"1.0","event_id":"sha256:1d5459390ccd4f5e4b5a0dc3d4bf4669c00217828e7348f8007b8affb1752625"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:QJPVO33YU24PFCGRN2V2LVPBOB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Reflection of a Point Object in an Arbitrary Curved Mirror","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.optics","authors_text":"Shikhar Mittal","submitted_at":"2019-03-04T05:14:32Z","abstract_excerpt":"In this work, I have derived the equation of the curve obtained on reflection of a point object in an arbitrary curved mirror if the object and the mirror are placed on the 2D Cartesian plane. I have used only the basic laws of reflection of classical geometric optics and elementary coordinate geometry. Several examples are provided and compared with Gaussian optics. We also see how the equations reduce to the standard mirror formula under the paraxial approximation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.01074","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":""},"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":"2026-05-17T23:52:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sWlCdlh4V14gxXKDVw6F+YncLryto6QafW/RNlrFgrNbCsBWxtoa5G34a0PfboGwwmYCAqGnBH3u++edteLVCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:33:15.818488Z"},"content_sha256":"3e7553a3b55a505e9c97a3a37ee19ac93c61643bfcc0aa541c7b7391cb780f1a","schema_version":"1.0","event_id":"sha256:3e7553a3b55a505e9c97a3a37ee19ac93c61643bfcc0aa541c7b7391cb780f1a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QJPVO33YU24PFCGRN2V2LVPBOB/bundle.json","state_url":"https://pith.science/pith/QJPVO33YU24PFCGRN2V2LVPBOB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QJPVO33YU24PFCGRN2V2LVPBOB/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":"2026-05-28T06:33:15Z","links":{"resolver":"https://pith.science/pith/QJPVO33YU24PFCGRN2V2LVPBOB","bundle":"https://pith.science/pith/QJPVO33YU24PFCGRN2V2LVPBOB/bundle.json","state":"https://pith.science/pith/QJPVO33YU24PFCGRN2V2LVPBOB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QJPVO33YU24PFCGRN2V2LVPBOB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:QJPVO33YU24PFCGRN2V2LVPBOB","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":"ba9dd8b2bb0b8591f009eabb41fc91319a9895e21649e42514486e536020376b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2019-03-04T05:14:32Z","title_canon_sha256":"8a9462c248a4c62d298297b082276d2a442d48355e2a24175a617b053d8a771a"},"schema_version":"1.0","source":{"id":"1903.01074","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.01074","created_at":"2026-05-17T23:52:12Z"},{"alias_kind":"arxiv_version","alias_value":"1903.01074v1","created_at":"2026-05-17T23:52:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.01074","created_at":"2026-05-17T23:52:12Z"},{"alias_kind":"pith_short_12","alias_value":"QJPVO33YU24P","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"QJPVO33YU24PFCGR","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"QJPVO33Y","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:3e7553a3b55a505e9c97a3a37ee19ac93c61643bfcc0aa541c7b7391cb780f1a","target":"graph","created_at":"2026-05-17T23:52:12Z","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":"In this work, I have derived the equation of the curve obtained on reflection of a point object in an arbitrary curved mirror if the object and the mirror are placed on the 2D Cartesian plane. I have used only the basic laws of reflection of classical geometric optics and elementary coordinate geometry. Several examples are provided and compared with Gaussian optics. We also see how the equations reduce to the standard mirror formula under the paraxial approximation.","authors_text":"Shikhar Mittal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2019-03-04T05:14:32Z","title":"Reflection of a Point Object in an Arbitrary Curved Mirror"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.01074","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":"sha256:1d5459390ccd4f5e4b5a0dc3d4bf4669c00217828e7348f8007b8affb1752625","target":"record","created_at":"2026-05-17T23:52:12Z","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":"ba9dd8b2bb0b8591f009eabb41fc91319a9895e21649e42514486e536020376b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2019-03-04T05:14:32Z","title_canon_sha256":"8a9462c248a4c62d298297b082276d2a442d48355e2a24175a617b053d8a771a"},"schema_version":"1.0","source":{"id":"1903.01074","kind":"arxiv","version":1}},"canonical_sha256":"825f576f78a6b8f288d16eaba5d5e1707a83ce3b4d1c2f00bff7261a4dbc3ad8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"825f576f78a6b8f288d16eaba5d5e1707a83ce3b4d1c2f00bff7261a4dbc3ad8","first_computed_at":"2026-05-17T23:52:12.387250Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:12.387250Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RXtBy2Nxtd1uZXhKwo+eWVdE0EUXKlkvLQrakDpbup4z7GoRJHzw/S3b4GKL/clA9EU9y3wvOQjp4kdp/rolAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:12.387928Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.01074","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d5459390ccd4f5e4b5a0dc3d4bf4669c00217828e7348f8007b8affb1752625","sha256:3e7553a3b55a505e9c97a3a37ee19ac93c61643bfcc0aa541c7b7391cb780f1a"],"state_sha256":"7500bcdc229e49048ee881916ef1ff0f0c5d1be22fc1b753f909902f2ace124f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NtIfapCMMNsoOSfFTTmTsn7CCSO680XrhxbzkIZWPtU4LNJLjrgHzUhSi/Qy0621Fp/zxL4rvEGSe6lzx1HpCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T06:33:15.821584Z","bundle_sha256":"d3e3ee815db50da9daed8fbdf1385718a671dca03a53d67fa57aeb0e9e3d5019"}}