{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:QWTJFBVAIOIHPKDX3KWAUXCBXS","short_pith_number":"pith:QWTJFBVA","canonical_record":{"source":{"id":"1802.02458","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2018-02-06T12:00:49Z","cross_cats_sorted":[],"title_canon_sha256":"10c4fce63a3ed4659b0eebe30d30a1115a8481eb20e1f095ed510a21d61c3253","abstract_canon_sha256":"2fe35d02b85243fc84f8419f24ecf989aa968b2f29d3214107896d18de64224f"},"schema_version":"1.0"},"canonical_sha256":"85a69286a0439077a877daac0a5c41bcadb9d87668062248efa3e4935f1d0364","source":{"kind":"arxiv","id":"1802.02458","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.02458","created_at":"2026-05-18T00:15:36Z"},{"alias_kind":"arxiv_version","alias_value":"1802.02458v2","created_at":"2026-05-18T00:15:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.02458","created_at":"2026-05-18T00:15:36Z"},{"alias_kind":"pith_short_12","alias_value":"QWTJFBVAIOIH","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"QWTJFBVAIOIHPKDX","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"QWTJFBVA","created_at":"2026-05-18T12:32:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:QWTJFBVAIOIHPKDX3KWAUXCBXS","target":"record","payload":{"canonical_record":{"source":{"id":"1802.02458","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2018-02-06T12:00:49Z","cross_cats_sorted":[],"title_canon_sha256":"10c4fce63a3ed4659b0eebe30d30a1115a8481eb20e1f095ed510a21d61c3253","abstract_canon_sha256":"2fe35d02b85243fc84f8419f24ecf989aa968b2f29d3214107896d18de64224f"},"schema_version":"1.0"},"canonical_sha256":"85a69286a0439077a877daac0a5c41bcadb9d87668062248efa3e4935f1d0364","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:36.663501Z","signature_b64":"0fDKYa+jA890xfBUGqgrNGx4yY9uT6j9c5c4VzWKySefpLr6L3XBE5Q8ChSVy3tZ+GCW7GZH0eQq79K12qiiCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85a69286a0439077a877daac0a5c41bcadb9d87668062248efa3e4935f1d0364","last_reissued_at":"2026-05-18T00:15:36.662730Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:36.662730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.02458","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":"2026-05-18T00:15:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9EJdrhG7+bQZFJ+genztVjm6ssU8hzM9YIwN0uJ0G+laQ96oFwE4dNoCtfZASLqxq2XLWuFVL0S7Vofg17oRBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T19:57:05.036042Z"},"content_sha256":"3d3b4e55c6d2de71c4f4dd6bcac2038db3e6746b3505fe5163f8d0601fed5af4","schema_version":"1.0","event_id":"sha256:3d3b4e55c6d2de71c4f4dd6bcac2038db3e6746b3505fe5163f8d0601fed5af4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:QWTJFBVAIOIHPKDX3KWAUXCBXS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Group theoretical formulation of free fall and projectile motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.gen-ph","authors_text":"Koray D\\\"uzta\\c{s}","submitted_at":"2018-02-06T12:00:49Z","abstract_excerpt":"In this work we formulate the group theoretical description of free fall and projectile motion. We show that the kinematic equations for constant acceleration form a one parameter group acting on a phase space. We define the group elements $\\phi_t$ by their action on the points in the phase space. We also generalize this approach to projectile motion. We evaluate the group orbits regarding their relations to the physical orbits of particles and unphysical solutions. We note that the group theoretical formulation does not apply to more general cases involving a time dependent acceleration. This"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.02458","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":""},"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":"2026-05-18T00:15:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9STFra20g/XVWIpd8RWROTPqrYVTdEkblsJPTxT8fGdChrCPrBGSV1Ct3EE6rSL/YeGqDuKfdWgdFOyKU/umAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T19:57:05.036421Z"},"content_sha256":"ae4ef6d46121dad7c1c9bcc5489c530a1e71c88310a22a58ecde50c024a8048a","schema_version":"1.0","event_id":"sha256:ae4ef6d46121dad7c1c9bcc5489c530a1e71c88310a22a58ecde50c024a8048a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QWTJFBVAIOIHPKDX3KWAUXCBXS/bundle.json","state_url":"https://pith.science/pith/QWTJFBVAIOIHPKDX3KWAUXCBXS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QWTJFBVAIOIHPKDX3KWAUXCBXS/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":"2026-06-10T19:57:05Z","links":{"resolver":"https://pith.science/pith/QWTJFBVAIOIHPKDX3KWAUXCBXS","bundle":"https://pith.science/pith/QWTJFBVAIOIHPKDX3KWAUXCBXS/bundle.json","state":"https://pith.science/pith/QWTJFBVAIOIHPKDX3KWAUXCBXS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QWTJFBVAIOIHPKDX3KWAUXCBXS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:QWTJFBVAIOIHPKDX3KWAUXCBXS","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":"2fe35d02b85243fc84f8419f24ecf989aa968b2f29d3214107896d18de64224f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2018-02-06T12:00:49Z","title_canon_sha256":"10c4fce63a3ed4659b0eebe30d30a1115a8481eb20e1f095ed510a21d61c3253"},"schema_version":"1.0","source":{"id":"1802.02458","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.02458","created_at":"2026-05-18T00:15:36Z"},{"alias_kind":"arxiv_version","alias_value":"1802.02458v2","created_at":"2026-05-18T00:15:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.02458","created_at":"2026-05-18T00:15:36Z"},{"alias_kind":"pith_short_12","alias_value":"QWTJFBVAIOIH","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"QWTJFBVAIOIHPKDX","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"QWTJFBVA","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:ae4ef6d46121dad7c1c9bcc5489c530a1e71c88310a22a58ecde50c024a8048a","target":"graph","created_at":"2026-05-18T00:15:36Z","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 we formulate the group theoretical description of free fall and projectile motion. We show that the kinematic equations for constant acceleration form a one parameter group acting on a phase space. We define the group elements $\\phi_t$ by their action on the points in the phase space. We also generalize this approach to projectile motion. We evaluate the group orbits regarding their relations to the physical orbits of particles and unphysical solutions. We note that the group theoretical formulation does not apply to more general cases involving a time dependent acceleration. This","authors_text":"Koray D\\\"uzta\\c{s}","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2018-02-06T12:00:49Z","title":"Group theoretical formulation of free fall and projectile motion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.02458","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":"sha256:3d3b4e55c6d2de71c4f4dd6bcac2038db3e6746b3505fe5163f8d0601fed5af4","target":"record","created_at":"2026-05-18T00:15:36Z","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":"2fe35d02b85243fc84f8419f24ecf989aa968b2f29d3214107896d18de64224f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2018-02-06T12:00:49Z","title_canon_sha256":"10c4fce63a3ed4659b0eebe30d30a1115a8481eb20e1f095ed510a21d61c3253"},"schema_version":"1.0","source":{"id":"1802.02458","kind":"arxiv","version":2}},"canonical_sha256":"85a69286a0439077a877daac0a5c41bcadb9d87668062248efa3e4935f1d0364","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85a69286a0439077a877daac0a5c41bcadb9d87668062248efa3e4935f1d0364","first_computed_at":"2026-05-18T00:15:36.662730Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:36.662730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0fDKYa+jA890xfBUGqgrNGx4yY9uT6j9c5c4VzWKySefpLr6L3XBE5Q8ChSVy3tZ+GCW7GZH0eQq79K12qiiCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:36.663501Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.02458","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d3b4e55c6d2de71c4f4dd6bcac2038db3e6746b3505fe5163f8d0601fed5af4","sha256:ae4ef6d46121dad7c1c9bcc5489c530a1e71c88310a22a58ecde50c024a8048a"],"state_sha256":"a60c5abd5c2175cc3706b39b86694f46267e532279fcedd0a20f38753f524990"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mXSDYNLcfChmfSGyrl+yOM01i7PKXLXoPG6bULD0UgVsD+cW3jvcJ5Mhkto/3KoREFBxdF0Lzq0EOWB/IT1vDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T19:57:05.038998Z","bundle_sha256":"fec716a66af3a13e55a9e05e7770b4aa6ba78ff0d2616ece9a25bbb2e5d3494c"}}