{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:GJ26RLGCVM45L6BCUGY4J6ZSAS","short_pith_number":"pith:GJ26RLGC","canonical_record":{"source":{"id":"1105.0313","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-05-02T12:53:25Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"d7da47bd8513c38ff6d2e1ff7fe6eb2b2b4b465103f52b28a86a1f36c159efb4","abstract_canon_sha256":"2cf4bd0c0fd6d672435e5d9ec96a6339c020c65f813ce17d0dba06fac07255b0"},"schema_version":"1.0"},"canonical_sha256":"3275e8acc2ab39d5f822a1b1c4fb320493b63f5c26f57ab1a3459b52fb55e5fd","source":{"kind":"arxiv","id":"1105.0313","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.0313","created_at":"2026-05-18T02:02:10Z"},{"alias_kind":"arxiv_version","alias_value":"1105.0313v2","created_at":"2026-05-18T02:02:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.0313","created_at":"2026-05-18T02:02:10Z"},{"alias_kind":"pith_short_12","alias_value":"GJ26RLGCVM45","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GJ26RLGCVM45L6BC","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GJ26RLGC","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:GJ26RLGCVM45L6BCUGY4J6ZSAS","target":"record","payload":{"canonical_record":{"source":{"id":"1105.0313","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-05-02T12:53:25Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"d7da47bd8513c38ff6d2e1ff7fe6eb2b2b4b465103f52b28a86a1f36c159efb4","abstract_canon_sha256":"2cf4bd0c0fd6d672435e5d9ec96a6339c020c65f813ce17d0dba06fac07255b0"},"schema_version":"1.0"},"canonical_sha256":"3275e8acc2ab39d5f822a1b1c4fb320493b63f5c26f57ab1a3459b52fb55e5fd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:02:10.282509Z","signature_b64":"vtjwLs1beFJrp2CaRMKagjz508ljwmQZVw1Ez4ZFnsKDevCg7oC4Zf5IukgEMQT+5hI6shaN0GgezhtAczq0Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3275e8acc2ab39d5f822a1b1c4fb320493b63f5c26f57ab1a3459b52fb55e5fd","last_reissued_at":"2026-05-18T02:02:10.281865Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:02:10.281865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.0313","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":"2026-05-18T02:02:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AjJHDuRAUa3Q+Sssc5S40tynQB48xSjKiq5oBAOI9D0M+HGL888t6bUa3xzlj/Y5llYGcCm2jgtPPECKp9bUAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T11:50:44.238233Z"},"content_sha256":"1d0218ed69537b73e35f4ca50ee8f58af869fc6365b5af25cc81fb4ced37babb","schema_version":"1.0","event_id":"sha256:1d0218ed69537b73e35f4ca50ee8f58af869fc6365b5af25cc81fb4ced37babb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:GJ26RLGCVM45L6BCUGY4J6ZSAS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Classical mechanics in reparametrization-invariant formulation and the Schr\\\"odinger equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"A. A. Deriglazov, B. F. Rizzuti","submitted_at":"2011-05-02T12:53:25Z","abstract_excerpt":"The dynamics of any classical-mechanics system can be formulated in the reparametrization-invariant (RI) form (that is we use the parametric representation for trajectories, ${\\bf x}={\\bf x}(\\tau)$, $t=t(\\tau)$ instead of ${\\bf x}={\\bf x}(t)$). In this pedagogical note we discuss what the quantization rules look like for the RI formulation of mechanics. We point out that in this case some of the rules acquire an intuitively clearer form. Hence the formulation could be an alternative starting point for teaching the basic principles of quantum mechanics. The advantages can be resumed as follows."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.0313","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":"2026-05-18T02:02:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I0VdO3RBPk70buR4QMu5w9YHxombJeNT7ewZVEdWHwMT6CTy2Q8esQIwseUfj4fzp7NYxiGYVOsa6Ocz7t8ICQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T11:50:44.238592Z"},"content_sha256":"23916143fce190ce528e6ede0c2b86d3b29b1791fa251ddeb7c478a0e40f8d6b","schema_version":"1.0","event_id":"sha256:23916143fce190ce528e6ede0c2b86d3b29b1791fa251ddeb7c478a0e40f8d6b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GJ26RLGCVM45L6BCUGY4J6ZSAS/bundle.json","state_url":"https://pith.science/pith/GJ26RLGCVM45L6BCUGY4J6ZSAS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GJ26RLGCVM45L6BCUGY4J6ZSAS/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":"2026-06-26T11:50:44Z","links":{"resolver":"https://pith.science/pith/GJ26RLGCVM45L6BCUGY4J6ZSAS","bundle":"https://pith.science/pith/GJ26RLGCVM45L6BCUGY4J6ZSAS/bundle.json","state":"https://pith.science/pith/GJ26RLGCVM45L6BCUGY4J6ZSAS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GJ26RLGCVM45L6BCUGY4J6ZSAS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GJ26RLGCVM45L6BCUGY4J6ZSAS","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":"2cf4bd0c0fd6d672435e5d9ec96a6339c020c65f813ce17d0dba06fac07255b0","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-05-02T12:53:25Z","title_canon_sha256":"d7da47bd8513c38ff6d2e1ff7fe6eb2b2b4b465103f52b28a86a1f36c159efb4"},"schema_version":"1.0","source":{"id":"1105.0313","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.0313","created_at":"2026-05-18T02:02:10Z"},{"alias_kind":"arxiv_version","alias_value":"1105.0313v2","created_at":"2026-05-18T02:02:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.0313","created_at":"2026-05-18T02:02:10Z"},{"alias_kind":"pith_short_12","alias_value":"GJ26RLGCVM45","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GJ26RLGCVM45L6BC","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GJ26RLGC","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:23916143fce190ce528e6ede0c2b86d3b29b1791fa251ddeb7c478a0e40f8d6b","target":"graph","created_at":"2026-05-18T02:02:10Z","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":"The dynamics of any classical-mechanics system can be formulated in the reparametrization-invariant (RI) form (that is we use the parametric representation for trajectories, ${\\bf x}={\\bf x}(\\tau)$, $t=t(\\tau)$ instead of ${\\bf x}={\\bf x}(t)$). In this pedagogical note we discuss what the quantization rules look like for the RI formulation of mechanics. We point out that in this case some of the rules acquire an intuitively clearer form. Hence the formulation could be an alternative starting point for teaching the basic principles of quantum mechanics. The advantages can be resumed as follows.","authors_text":"A. A. Deriglazov, B. F. Rizzuti","cross_cats":["math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-05-02T12:53:25Z","title":"Classical mechanics in reparametrization-invariant formulation and the Schr\\\"odinger equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.0313","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":"sha256:1d0218ed69537b73e35f4ca50ee8f58af869fc6365b5af25cc81fb4ced37babb","target":"record","created_at":"2026-05-18T02:02:10Z","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":"2cf4bd0c0fd6d672435e5d9ec96a6339c020c65f813ce17d0dba06fac07255b0","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-05-02T12:53:25Z","title_canon_sha256":"d7da47bd8513c38ff6d2e1ff7fe6eb2b2b4b465103f52b28a86a1f36c159efb4"},"schema_version":"1.0","source":{"id":"1105.0313","kind":"arxiv","version":2}},"canonical_sha256":"3275e8acc2ab39d5f822a1b1c4fb320493b63f5c26f57ab1a3459b52fb55e5fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3275e8acc2ab39d5f822a1b1c4fb320493b63f5c26f57ab1a3459b52fb55e5fd","first_computed_at":"2026-05-18T02:02:10.281865Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:02:10.281865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vtjwLs1beFJrp2CaRMKagjz508ljwmQZVw1Ez4ZFnsKDevCg7oC4Zf5IukgEMQT+5hI6shaN0GgezhtAczq0Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:02:10.282509Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.0313","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d0218ed69537b73e35f4ca50ee8f58af869fc6365b5af25cc81fb4ced37babb","sha256:23916143fce190ce528e6ede0c2b86d3b29b1791fa251ddeb7c478a0e40f8d6b"],"state_sha256":"613d1283bd9c9f9e98c1a223967059152f23f683ac69ea84727d532c8840aa93"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mZDOJbkYbSsYqAn8qep7jgrLUj42+cT3ZNa+E/F9Cq3qpvqSQ4ZgxLqiI+CADhYFr1XlptdMsXaXyHBXCcLICw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T11:50:44.240713Z","bundle_sha256":"4a762d23e120dddd73ef22a2c2b5427bd10b811edccb52a34de71ef157a701ce"}}