{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:FHWLD2TKKGMZRWMEWMDALY4G3L","short_pith_number":"pith:FHWLD2TK","canonical_record":{"source":{"id":"1503.03403","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.HC","submitted_at":"2015-03-11T16:20:51Z","cross_cats_sorted":["math.HO"],"title_canon_sha256":"b43499d365f51338d41aaa0144e9b024134e845cb579bb71db7369f777ee9856","abstract_canon_sha256":"8060f3ca59a6446e8a6faafd6ad3d45adf76636b104fa9e4ba8621c1587b6839"},"schema_version":"1.0"},"canonical_sha256":"29ecb1ea6a519998d984b30605e386dac43f79570c09f043432d53eb38f824e1","source":{"kind":"arxiv","id":"1503.03403","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.03403","created_at":"2026-05-18T01:34:34Z"},{"alias_kind":"arxiv_version","alias_value":"1503.03403v2","created_at":"2026-05-18T01:34:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.03403","created_at":"2026-05-18T01:34:34Z"},{"alias_kind":"pith_short_12","alias_value":"FHWLD2TKKGMZ","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FHWLD2TKKGMZRWME","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FHWLD2TK","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:FHWLD2TKKGMZRWMEWMDALY4G3L","target":"record","payload":{"canonical_record":{"source":{"id":"1503.03403","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.HC","submitted_at":"2015-03-11T16:20:51Z","cross_cats_sorted":["math.HO"],"title_canon_sha256":"b43499d365f51338d41aaa0144e9b024134e845cb579bb71db7369f777ee9856","abstract_canon_sha256":"8060f3ca59a6446e8a6faafd6ad3d45adf76636b104fa9e4ba8621c1587b6839"},"schema_version":"1.0"},"canonical_sha256":"29ecb1ea6a519998d984b30605e386dac43f79570c09f043432d53eb38f824e1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:34.976534Z","signature_b64":"f3xx1e1cGqMxAQI+GQiW/+rWhcQlssm09Qy35VFJadcTR9HUd93T5grNUayhnGCOdWFoDeZ9dESEOwTuU05OCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"29ecb1ea6a519998d984b30605e386dac43f79570c09f043432d53eb38f824e1","last_reissued_at":"2026-05-18T01:34:34.975916Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:34.975916Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.03403","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":"2026-05-18T01:34:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SAr7Skg19zv58R/2jhshygNhinwANHmJl6MMf8fydQrIWdBEpACXqriByfsyF8Y/fs70wQdEYUAyVn2LKH8KDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T23:19:19.431011Z"},"content_sha256":"581acbdecafbfcae0d51c448617dcab7def0e5de1707a5197709c4f4e6174c48","schema_version":"1.0","event_id":"sha256:581acbdecafbfcae0d51c448617dcab7def0e5de1707a5197709c4f4e6174c48"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:FHWLD2TKKGMZRWMEWMDALY4G3L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bublz! : Playing with Bubbles to Develop Mathematical Thinking","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.HO"],"primary_cat":"cs.HC","authors_text":"Dhruv Chand, Karthik Gopalakrishnan, Mudit Sinha, Nisha KK, Shreya Sriram","submitted_at":"2015-03-11T16:20:51Z","abstract_excerpt":"We encounter mathematical problems in various forms in our lives, thus making mathematical thinking an important human ability. In this paper, we present Bublz!, a simple, click-driven game for children to engage in and develop mathematical thinking in an enjoyable manner."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03403","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":"2026-05-18T01:34:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2Ay6Vwcks4UaqeES41bduBnLYBLPwXV5JySBxUUh90/6ceh2ANSsv2UqUwDxmMZT3InaHCfq6GmYJLHLNYKZAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T23:19:19.431670Z"},"content_sha256":"94071f19457b07baba2b8c040925da446262eb33a8a294c8ba13c1703f0cff7f","schema_version":"1.0","event_id":"sha256:94071f19457b07baba2b8c040925da446262eb33a8a294c8ba13c1703f0cff7f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FHWLD2TKKGMZRWMEWMDALY4G3L/bundle.json","state_url":"https://pith.science/pith/FHWLD2TKKGMZRWMEWMDALY4G3L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FHWLD2TKKGMZRWMEWMDALY4G3L/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":"2026-05-27T23:19:19Z","links":{"resolver":"https://pith.science/pith/FHWLD2TKKGMZRWMEWMDALY4G3L","bundle":"https://pith.science/pith/FHWLD2TKKGMZRWMEWMDALY4G3L/bundle.json","state":"https://pith.science/pith/FHWLD2TKKGMZRWMEWMDALY4G3L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FHWLD2TKKGMZRWMEWMDALY4G3L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FHWLD2TKKGMZRWMEWMDALY4G3L","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":"8060f3ca59a6446e8a6faafd6ad3d45adf76636b104fa9e4ba8621c1587b6839","cross_cats_sorted":["math.HO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.HC","submitted_at":"2015-03-11T16:20:51Z","title_canon_sha256":"b43499d365f51338d41aaa0144e9b024134e845cb579bb71db7369f777ee9856"},"schema_version":"1.0","source":{"id":"1503.03403","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.03403","created_at":"2026-05-18T01:34:34Z"},{"alias_kind":"arxiv_version","alias_value":"1503.03403v2","created_at":"2026-05-18T01:34:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.03403","created_at":"2026-05-18T01:34:34Z"},{"alias_kind":"pith_short_12","alias_value":"FHWLD2TKKGMZ","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FHWLD2TKKGMZRWME","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FHWLD2TK","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:94071f19457b07baba2b8c040925da446262eb33a8a294c8ba13c1703f0cff7f","target":"graph","created_at":"2026-05-18T01:34:34Z","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":"We encounter mathematical problems in various forms in our lives, thus making mathematical thinking an important human ability. In this paper, we present Bublz!, a simple, click-driven game for children to engage in and develop mathematical thinking in an enjoyable manner.","authors_text":"Dhruv Chand, Karthik Gopalakrishnan, Mudit Sinha, Nisha KK, Shreya Sriram","cross_cats":["math.HO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.HC","submitted_at":"2015-03-11T16:20:51Z","title":"Bublz! : Playing with Bubbles to Develop Mathematical Thinking"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03403","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":"sha256:581acbdecafbfcae0d51c448617dcab7def0e5de1707a5197709c4f4e6174c48","target":"record","created_at":"2026-05-18T01:34:34Z","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":"8060f3ca59a6446e8a6faafd6ad3d45adf76636b104fa9e4ba8621c1587b6839","cross_cats_sorted":["math.HO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.HC","submitted_at":"2015-03-11T16:20:51Z","title_canon_sha256":"b43499d365f51338d41aaa0144e9b024134e845cb579bb71db7369f777ee9856"},"schema_version":"1.0","source":{"id":"1503.03403","kind":"arxiv","version":2}},"canonical_sha256":"29ecb1ea6a519998d984b30605e386dac43f79570c09f043432d53eb38f824e1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"29ecb1ea6a519998d984b30605e386dac43f79570c09f043432d53eb38f824e1","first_computed_at":"2026-05-18T01:34:34.975916Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:34.975916Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f3xx1e1cGqMxAQI+GQiW/+rWhcQlssm09Qy35VFJadcTR9HUd93T5grNUayhnGCOdWFoDeZ9dESEOwTuU05OCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:34.976534Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.03403","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:581acbdecafbfcae0d51c448617dcab7def0e5de1707a5197709c4f4e6174c48","sha256:94071f19457b07baba2b8c040925da446262eb33a8a294c8ba13c1703f0cff7f"],"state_sha256":"ea15b11e5118653fa24cce19ab55a2b8ffaa39be7857b45323ebf4c644e26359"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jd9jA3klYUD0ifzhkEHBL6C1CzIv1hn2e79Zd4VtOwDmw2NUPFtSJJsvP7mmPWnUfk569/HPcHhOLTqhgHh/DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T23:19:19.435219Z","bundle_sha256":"644f7a4efe518e77a7f14b4d374e8a72dd1d2520dd0e4621bd7ed2b0e976c58a"}}