{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:KMYXUKGB7I6SMXWWOUVZK3GKOV","short_pith_number":"pith:KMYXUKGB","canonical_record":{"source":{"id":"1505.04750","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-05-18T18:31:27Z","cross_cats_sorted":[],"title_canon_sha256":"a601394ee73d7909802d6d5736665b9c7c4c37baa985258545e485f6489b57f8","abstract_canon_sha256":"3aedd65949fdb44b3e81d4533953dffae8430555b6ceff37f04ee83e39af8e31"},"schema_version":"1.0"},"canonical_sha256":"53317a28c1fa3d265ed6752b956cca754b2262a7d379381e07ab87a3a282342d","source":{"kind":"arxiv","id":"1505.04750","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.04750","created_at":"2026-05-18T00:53:35Z"},{"alias_kind":"arxiv_version","alias_value":"1505.04750v1","created_at":"2026-05-18T00:53:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.04750","created_at":"2026-05-18T00:53:35Z"},{"alias_kind":"pith_short_12","alias_value":"KMYXUKGB7I6S","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KMYXUKGB7I6SMXWW","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KMYXUKGB","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:KMYXUKGB7I6SMXWWOUVZK3GKOV","target":"record","payload":{"canonical_record":{"source":{"id":"1505.04750","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-05-18T18:31:27Z","cross_cats_sorted":[],"title_canon_sha256":"a601394ee73d7909802d6d5736665b9c7c4c37baa985258545e485f6489b57f8","abstract_canon_sha256":"3aedd65949fdb44b3e81d4533953dffae8430555b6ceff37f04ee83e39af8e31"},"schema_version":"1.0"},"canonical_sha256":"53317a28c1fa3d265ed6752b956cca754b2262a7d379381e07ab87a3a282342d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:35.060618Z","signature_b64":"aaIUL0Wd+UqGyj8heBJRpRX3dGmQRBZi2wDfRC+XQYtQHqtFY68WTVCataD9U3PDySh5fc1apNPjegrma+5HBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53317a28c1fa3d265ed6752b956cca754b2262a7d379381e07ab87a3a282342d","last_reissued_at":"2026-05-18T00:53:35.060200Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:35.060200Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.04750","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":"2026-05-18T00:53:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VMk3AGzXzkbqOAj++s1WxX4KkGxvz4RDqjytFfePQM2bFYvjT/MvITi3VszmGjzCFgxq+k0OCDfbB9ez3uHjDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T14:30:07.456788Z"},"content_sha256":"9c3fbde397bd98d8616abc3a154eeb2891892daa4b97c286705672981f64bc1e","schema_version":"1.0","event_id":"sha256:9c3fbde397bd98d8616abc3a154eeb2891892daa4b97c286705672981f64bc1e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:KMYXUKGB7I6SMXWWOUVZK3GKOV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Time of falling of a quantum particle into an inverse square potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Vasyl Vasyuta, Volodymyr Tkachuk","submitted_at":"2015-05-18T18:31:27Z","abstract_excerpt":"Evolution of a particle in an inverse square potential is studied. We derive an equation of motion for $\\left<r^2\\right>$ and solve it exactly. It gives us a possibility to identify the conditions under which a falling of a quantum particle into an attractive centre is possible. We get the time of falling of a particle from an initial state into the centre. An example of a quasi-stationary state which evolves with $\\left<r^2\\right>$ being constant in time is given. We demonstrate the existence of quantum limit of falling, namely, a particle does not fall into the attractive centre, when coupli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04750","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":"2026-05-18T00:53:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+lIY1oSe7dDYMeXI/uJWjw2K5uXIA+8gPkxsTOXU6I2xsC7gYyurU0xloJkQ9ydHgl0s+9fq7Tx+eFx/+3oqAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T14:30:07.457133Z"},"content_sha256":"03c43ec611075062e60d4e5ababec2d7a713f80b7f406c46ea3d8433998f4056","schema_version":"1.0","event_id":"sha256:03c43ec611075062e60d4e5ababec2d7a713f80b7f406c46ea3d8433998f4056"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KMYXUKGB7I6SMXWWOUVZK3GKOV/bundle.json","state_url":"https://pith.science/pith/KMYXUKGB7I6SMXWWOUVZK3GKOV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KMYXUKGB7I6SMXWWOUVZK3GKOV/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":"2026-06-05T14:30:07Z","links":{"resolver":"https://pith.science/pith/KMYXUKGB7I6SMXWWOUVZK3GKOV","bundle":"https://pith.science/pith/KMYXUKGB7I6SMXWWOUVZK3GKOV/bundle.json","state":"https://pith.science/pith/KMYXUKGB7I6SMXWWOUVZK3GKOV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KMYXUKGB7I6SMXWWOUVZK3GKOV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:KMYXUKGB7I6SMXWWOUVZK3GKOV","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":"3aedd65949fdb44b3e81d4533953dffae8430555b6ceff37f04ee83e39af8e31","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-05-18T18:31:27Z","title_canon_sha256":"a601394ee73d7909802d6d5736665b9c7c4c37baa985258545e485f6489b57f8"},"schema_version":"1.0","source":{"id":"1505.04750","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.04750","created_at":"2026-05-18T00:53:35Z"},{"alias_kind":"arxiv_version","alias_value":"1505.04750v1","created_at":"2026-05-18T00:53:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.04750","created_at":"2026-05-18T00:53:35Z"},{"alias_kind":"pith_short_12","alias_value":"KMYXUKGB7I6S","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KMYXUKGB7I6SMXWW","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KMYXUKGB","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:03c43ec611075062e60d4e5ababec2d7a713f80b7f406c46ea3d8433998f4056","target":"graph","created_at":"2026-05-18T00:53:35Z","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":"Evolution of a particle in an inverse square potential is studied. We derive an equation of motion for $\\left<r^2\\right>$ and solve it exactly. It gives us a possibility to identify the conditions under which a falling of a quantum particle into an attractive centre is possible. We get the time of falling of a particle from an initial state into the centre. An example of a quasi-stationary state which evolves with $\\left<r^2\\right>$ being constant in time is given. We demonstrate the existence of quantum limit of falling, namely, a particle does not fall into the attractive centre, when coupli","authors_text":"Vasyl Vasyuta, Volodymyr Tkachuk","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-05-18T18:31:27Z","title":"Time of falling of a quantum particle into an inverse square potential"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04750","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":"sha256:9c3fbde397bd98d8616abc3a154eeb2891892daa4b97c286705672981f64bc1e","target":"record","created_at":"2026-05-18T00:53:35Z","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":"3aedd65949fdb44b3e81d4533953dffae8430555b6ceff37f04ee83e39af8e31","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-05-18T18:31:27Z","title_canon_sha256":"a601394ee73d7909802d6d5736665b9c7c4c37baa985258545e485f6489b57f8"},"schema_version":"1.0","source":{"id":"1505.04750","kind":"arxiv","version":1}},"canonical_sha256":"53317a28c1fa3d265ed6752b956cca754b2262a7d379381e07ab87a3a282342d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"53317a28c1fa3d265ed6752b956cca754b2262a7d379381e07ab87a3a282342d","first_computed_at":"2026-05-18T00:53:35.060200Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:35.060200Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aaIUL0Wd+UqGyj8heBJRpRX3dGmQRBZi2wDfRC+XQYtQHqtFY68WTVCataD9U3PDySh5fc1apNPjegrma+5HBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:35.060618Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.04750","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c3fbde397bd98d8616abc3a154eeb2891892daa4b97c286705672981f64bc1e","sha256:03c43ec611075062e60d4e5ababec2d7a713f80b7f406c46ea3d8433998f4056"],"state_sha256":"e17c2e9505836c349d86dfbbd5310067e90a5da35e5f2de12970dad14c504f2b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1tkqBf6CYhBcY6Z47DccJTxrsn2cOGotlHNNEKVwedwxk7i917YYQWCz/2oauJRTjscP0LFDMQiveUn3yFMQDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T14:30:07.459122Z","bundle_sha256":"11f75347e1edc1caf29edc4d71d430855a94e409f017660701abf0ccd7c18167"}}