{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:TLQDEC4ST3TIKFLSBSZK6K2WTM","short_pith_number":"pith:TLQDEC4S","canonical_record":{"source":{"id":"1103.1208","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-03-07T08:05:08Z","cross_cats_sorted":["nlin.CG"],"title_canon_sha256":"371e3f424cf05705e97162575bf1a022050e69a71ecb0287d7cb26dde13c3686","abstract_canon_sha256":"6bfd2cfa0c62c98fd3bfec7817c47b4402dd69f1c6e3177c73bfd66661dfdac8"},"schema_version":"1.0"},"canonical_sha256":"9ae0320b929ee68515720cb2af2b569b0991d0c898466fed3a24de3486b141c9","source":{"kind":"arxiv","id":"1103.1208","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.1208","created_at":"2026-05-18T03:51:58Z"},{"alias_kind":"arxiv_version","alias_value":"1103.1208v1","created_at":"2026-05-18T03:51:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.1208","created_at":"2026-05-18T03:51:58Z"},{"alias_kind":"pith_short_12","alias_value":"TLQDEC4ST3TI","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TLQDEC4ST3TIKFLS","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TLQDEC4S","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:TLQDEC4ST3TIKFLSBSZK6K2WTM","target":"record","payload":{"canonical_record":{"source":{"id":"1103.1208","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-03-07T08:05:08Z","cross_cats_sorted":["nlin.CG"],"title_canon_sha256":"371e3f424cf05705e97162575bf1a022050e69a71ecb0287d7cb26dde13c3686","abstract_canon_sha256":"6bfd2cfa0c62c98fd3bfec7817c47b4402dd69f1c6e3177c73bfd66661dfdac8"},"schema_version":"1.0"},"canonical_sha256":"9ae0320b929ee68515720cb2af2b569b0991d0c898466fed3a24de3486b141c9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:51:58.676988Z","signature_b64":"icNd5hd/u2vJnIvEu6exnhqt/Rm7RCPp+SOljzBHwXisV/bGe+MtXbFzA9J5YRscf0hS30hzRgOjW+CVCSOLAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ae0320b929ee68515720cb2af2b569b0991d0c898466fed3a24de3486b141c9","last_reissued_at":"2026-05-18T03:51:58.676252Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:51:58.676252Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.1208","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":"2026-05-18T03:51:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sY+5FHjWyXb4juG2eCRJVlk6f+nMM0wuZktPxRAFlw+uzSh39MTIbbcMdgg6D2h0zcGAcxEUmO8RRcGC5z5DCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T11:02:52.296715Z"},"content_sha256":"6994dee04734b6858a8ad067c1a324fb9609738c856698be0b67530be9cae1c5","schema_version":"1.0","event_id":"sha256:6994dee04734b6858a8ad067c1a324fb9609738c856698be0b67530be9cae1c5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:TLQDEC4ST3TIKFLSBSZK6K2WTM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fractal behind smart shopping","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.CG"],"primary_cat":"cs.DM","authors_text":"Ken Yamamoto, Yoshihiro Yamazaki","submitted_at":"2011-03-07T08:05:08Z","abstract_excerpt":"The 'minimal' payment - a payment method which minimizes the number of coins in a purse - is presented. We focus on a time series of change given back to a shopper repeating the minimal payment. The delay plot shows visually that the set of successive change possesses a fine structure similar to the Sierpinski gasket. We also estimate effectivity of the minimal-payment method by means of the average number of coins in a purse, and conclude that the minimal-payment strategy is the best to reduce the number of coins in a purse. Moreover, we compare our results to the rule-60 cellular automaton a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.1208","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":"2026-05-18T03:51:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NA32PmmKrQuVHvHY1s6LCE51FTiemRosOrIU3V+X+HUMYwb2yAWWNkc/P0bQPnCKNdBDdMYPz1ZiBiRjF04hDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T11:02:52.297399Z"},"content_sha256":"6c4187885d445b67b47b90cb024136b1d94eecf9411d3d2550f86942b5efc011","schema_version":"1.0","event_id":"sha256:6c4187885d445b67b47b90cb024136b1d94eecf9411d3d2550f86942b5efc011"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TLQDEC4ST3TIKFLSBSZK6K2WTM/bundle.json","state_url":"https://pith.science/pith/TLQDEC4ST3TIKFLSBSZK6K2WTM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TLQDEC4ST3TIKFLSBSZK6K2WTM/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":"2026-06-07T11:02:52Z","links":{"resolver":"https://pith.science/pith/TLQDEC4ST3TIKFLSBSZK6K2WTM","bundle":"https://pith.science/pith/TLQDEC4ST3TIKFLSBSZK6K2WTM/bundle.json","state":"https://pith.science/pith/TLQDEC4ST3TIKFLSBSZK6K2WTM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TLQDEC4ST3TIKFLSBSZK6K2WTM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:TLQDEC4ST3TIKFLSBSZK6K2WTM","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":"6bfd2cfa0c62c98fd3bfec7817c47b4402dd69f1c6e3177c73bfd66661dfdac8","cross_cats_sorted":["nlin.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-03-07T08:05:08Z","title_canon_sha256":"371e3f424cf05705e97162575bf1a022050e69a71ecb0287d7cb26dde13c3686"},"schema_version":"1.0","source":{"id":"1103.1208","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.1208","created_at":"2026-05-18T03:51:58Z"},{"alias_kind":"arxiv_version","alias_value":"1103.1208v1","created_at":"2026-05-18T03:51:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.1208","created_at":"2026-05-18T03:51:58Z"},{"alias_kind":"pith_short_12","alias_value":"TLQDEC4ST3TI","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TLQDEC4ST3TIKFLS","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TLQDEC4S","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:6c4187885d445b67b47b90cb024136b1d94eecf9411d3d2550f86942b5efc011","target":"graph","created_at":"2026-05-18T03:51:58Z","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 'minimal' payment - a payment method which minimizes the number of coins in a purse - is presented. We focus on a time series of change given back to a shopper repeating the minimal payment. The delay plot shows visually that the set of successive change possesses a fine structure similar to the Sierpinski gasket. We also estimate effectivity of the minimal-payment method by means of the average number of coins in a purse, and conclude that the minimal-payment strategy is the best to reduce the number of coins in a purse. Moreover, we compare our results to the rule-60 cellular automaton a","authors_text":"Ken Yamamoto, Yoshihiro Yamazaki","cross_cats":["nlin.CG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-03-07T08:05:08Z","title":"Fractal behind smart shopping"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.1208","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":"sha256:6994dee04734b6858a8ad067c1a324fb9609738c856698be0b67530be9cae1c5","target":"record","created_at":"2026-05-18T03:51:58Z","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":"6bfd2cfa0c62c98fd3bfec7817c47b4402dd69f1c6e3177c73bfd66661dfdac8","cross_cats_sorted":["nlin.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-03-07T08:05:08Z","title_canon_sha256":"371e3f424cf05705e97162575bf1a022050e69a71ecb0287d7cb26dde13c3686"},"schema_version":"1.0","source":{"id":"1103.1208","kind":"arxiv","version":1}},"canonical_sha256":"9ae0320b929ee68515720cb2af2b569b0991d0c898466fed3a24de3486b141c9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ae0320b929ee68515720cb2af2b569b0991d0c898466fed3a24de3486b141c9","first_computed_at":"2026-05-18T03:51:58.676252Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:58.676252Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"icNd5hd/u2vJnIvEu6exnhqt/Rm7RCPp+SOljzBHwXisV/bGe+MtXbFzA9J5YRscf0hS30hzRgOjW+CVCSOLAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:58.676988Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.1208","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6994dee04734b6858a8ad067c1a324fb9609738c856698be0b67530be9cae1c5","sha256:6c4187885d445b67b47b90cb024136b1d94eecf9411d3d2550f86942b5efc011"],"state_sha256":"3704005b783fa8aad3df1fac642798c1527bdeeeab97b2c4051e0866a952f452"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kPdpPBPOR5LB1CQ9nZx4PkRtOo83OIPsXBQi6Gs815BL11IWnchtg4shPWGrFEEa1FUZZoSEgnkVDtnSQm8nBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T11:02:52.300747Z","bundle_sha256":"2a79fac6eba812eec0105084aed202a3af25a6146160ef28bf014249b824ebb4"}}