{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:BPUACTQS3SM2UIRGVKBPXHNQQ3","short_pith_number":"pith:BPUACTQS","canonical_record":{"source":{"id":"1201.3500","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-01-17T12:50:38Z","cross_cats_sorted":[],"title_canon_sha256":"3031ccad84fc45fb8183e56e9ce5c813a709fb84ca811219fb0b66478eadbf21","abstract_canon_sha256":"f404ee072fe578aa838d375a2c8ae15466112d16af23dac3789c2ff7d8adb5b7"},"schema_version":"1.0"},"canonical_sha256":"0be8014e12dc99aa2226aa82fb9db086c4278922d45961207c895a8cd6c5212f","source":{"kind":"arxiv","id":"1201.3500","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.3500","created_at":"2026-05-18T04:04:29Z"},{"alias_kind":"arxiv_version","alias_value":"1201.3500v1","created_at":"2026-05-18T04:04:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.3500","created_at":"2026-05-18T04:04:29Z"},{"alias_kind":"pith_short_12","alias_value":"BPUACTQS3SM2","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"BPUACTQS3SM2UIRG","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"BPUACTQS","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:BPUACTQS3SM2UIRGVKBPXHNQQ3","target":"record","payload":{"canonical_record":{"source":{"id":"1201.3500","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-01-17T12:50:38Z","cross_cats_sorted":[],"title_canon_sha256":"3031ccad84fc45fb8183e56e9ce5c813a709fb84ca811219fb0b66478eadbf21","abstract_canon_sha256":"f404ee072fe578aa838d375a2c8ae15466112d16af23dac3789c2ff7d8adb5b7"},"schema_version":"1.0"},"canonical_sha256":"0be8014e12dc99aa2226aa82fb9db086c4278922d45961207c895a8cd6c5212f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:04:29.066577Z","signature_b64":"1Y+aTJYGzdKYWubPX3hDhOF1xYinzsIR5PtoyRdIW8ieEmfL3+JSGuEnxDtXwmRVLxGzH2Oxtd1LjCV2Fb/aAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0be8014e12dc99aa2226aa82fb9db086c4278922d45961207c895a8cd6c5212f","last_reissued_at":"2026-05-18T04:04:29.065824Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:04:29.065824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.3500","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":"2026-05-18T04:04:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pPtaHjTpD5o7sv9HeABf38QGYkoHjQPG+nt9JWWC9/WfT3PCunmwty7rDBFEBclmoH7PhtHdAb7vudNGJwU+Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T17:30:49.137514Z"},"content_sha256":"e397c8ebc0ff93e26a4560c78b34f41fe3213b84f08c464bfa640375f0f63a2f","schema_version":"1.0","event_id":"sha256:e397c8ebc0ff93e26a4560c78b34f41fe3213b84f08c464bfa640375f0f63a2f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:BPUACTQS3SM2UIRGVKBPXHNQQ3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multiresolution Analysis Based on Coalescence Hidden-variable FIF","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"G. P. Kapoor, Srijanani Anurag Prasad","submitted_at":"2012-01-17T12:50:38Z","abstract_excerpt":"In the present paper, multiresolution analysis arising from Coalescence Hidden-variable Fractal Interpolation Functions (CHFIFs) is accomplished. The availability of a larger set of free variables and constrained variables with CHFIF in multiresolution analysis based on CHFIFs provides more control in reconstruction of functions in L2(\\mathbb{R})than that provided by multiresolution analysis based only on Affine Fractal Interpolation Functions (AFIFs). In our approach, the vector space of CHFIFs is introduced, its dimension is determined and Riesz bases of vector subspaces Vk, k \\in \\mathbb{Z}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3500","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":"2026-05-18T04:04:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uPBCdVgDP2opX7ADCJ4Ywv3DYf6uyd/kWzFTA2PmaS+aeNG0/qKmaMQqh4rTTxxW8b/jzrBPqz/eJ7Erjnl0Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T17:30:49.137850Z"},"content_sha256":"4bbe444106cdcc0f30a11d9edf037d451f86e4fd3c824c9656fe5bb5e6de268a","schema_version":"1.0","event_id":"sha256:4bbe444106cdcc0f30a11d9edf037d451f86e4fd3c824c9656fe5bb5e6de268a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BPUACTQS3SM2UIRGVKBPXHNQQ3/bundle.json","state_url":"https://pith.science/pith/BPUACTQS3SM2UIRGVKBPXHNQQ3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BPUACTQS3SM2UIRGVKBPXHNQQ3/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":"2026-06-01T17:30:49Z","links":{"resolver":"https://pith.science/pith/BPUACTQS3SM2UIRGVKBPXHNQQ3","bundle":"https://pith.science/pith/BPUACTQS3SM2UIRGVKBPXHNQQ3/bundle.json","state":"https://pith.science/pith/BPUACTQS3SM2UIRGVKBPXHNQQ3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BPUACTQS3SM2UIRGVKBPXHNQQ3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:BPUACTQS3SM2UIRGVKBPXHNQQ3","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":"f404ee072fe578aa838d375a2c8ae15466112d16af23dac3789c2ff7d8adb5b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-01-17T12:50:38Z","title_canon_sha256":"3031ccad84fc45fb8183e56e9ce5c813a709fb84ca811219fb0b66478eadbf21"},"schema_version":"1.0","source":{"id":"1201.3500","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.3500","created_at":"2026-05-18T04:04:29Z"},{"alias_kind":"arxiv_version","alias_value":"1201.3500v1","created_at":"2026-05-18T04:04:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.3500","created_at":"2026-05-18T04:04:29Z"},{"alias_kind":"pith_short_12","alias_value":"BPUACTQS3SM2","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"BPUACTQS3SM2UIRG","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"BPUACTQS","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:4bbe444106cdcc0f30a11d9edf037d451f86e4fd3c824c9656fe5bb5e6de268a","target":"graph","created_at":"2026-05-18T04:04:29Z","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 the present paper, multiresolution analysis arising from Coalescence Hidden-variable Fractal Interpolation Functions (CHFIFs) is accomplished. The availability of a larger set of free variables and constrained variables with CHFIF in multiresolution analysis based on CHFIFs provides more control in reconstruction of functions in L2(\\mathbb{R})than that provided by multiresolution analysis based only on Affine Fractal Interpolation Functions (AFIFs). In our approach, the vector space of CHFIFs is introduced, its dimension is determined and Riesz bases of vector subspaces Vk, k \\in \\mathbb{Z}","authors_text":"G. P. Kapoor, Srijanani Anurag Prasad","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-01-17T12:50:38Z","title":"Multiresolution Analysis Based on Coalescence Hidden-variable FIF"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3500","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:e397c8ebc0ff93e26a4560c78b34f41fe3213b84f08c464bfa640375f0f63a2f","target":"record","created_at":"2026-05-18T04:04:29Z","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":"f404ee072fe578aa838d375a2c8ae15466112d16af23dac3789c2ff7d8adb5b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-01-17T12:50:38Z","title_canon_sha256":"3031ccad84fc45fb8183e56e9ce5c813a709fb84ca811219fb0b66478eadbf21"},"schema_version":"1.0","source":{"id":"1201.3500","kind":"arxiv","version":1}},"canonical_sha256":"0be8014e12dc99aa2226aa82fb9db086c4278922d45961207c895a8cd6c5212f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0be8014e12dc99aa2226aa82fb9db086c4278922d45961207c895a8cd6c5212f","first_computed_at":"2026-05-18T04:04:29.065824Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:04:29.065824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1Y+aTJYGzdKYWubPX3hDhOF1xYinzsIR5PtoyRdIW8ieEmfL3+JSGuEnxDtXwmRVLxGzH2Oxtd1LjCV2Fb/aAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:04:29.066577Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.3500","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e397c8ebc0ff93e26a4560c78b34f41fe3213b84f08c464bfa640375f0f63a2f","sha256:4bbe444106cdcc0f30a11d9edf037d451f86e4fd3c824c9656fe5bb5e6de268a"],"state_sha256":"f747b5ad4d1b5acc267c9c40ecb1210a368a92e9cd3ba8635c3e581a5c44cc8b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1+pG76LquNxKX+H4VHuh5N4vBeE43a7qzjBiG3RnbUaW9NptW0QfTmT7ubUnEXIrHQuV9oUq9c1r61yI0ISRCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T17:30:49.139644Z","bundle_sha256":"1b07493622bf0bac65180e49dea188f0cdd56050b76526890f92c17d6a4101b1"}}