{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:KHLIMLKXAP5CHHR4H5GBYRXWNI","short_pith_number":"pith:KHLIMLKX","canonical_record":{"source":{"id":"1210.0405","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-01T13:57:34Z","cross_cats_sorted":[],"title_canon_sha256":"52dd7d389235edc4228b2c9cdb658870c79def85fe4ae8b815d4b2a59e95f673","abstract_canon_sha256":"2ee4dc588b6ab4db321d55fd3b02a1d53e215f5f2dc241a8b6f6e545f2040368"},"schema_version":"1.0"},"canonical_sha256":"51d6862d5703fa239e3c3f4c1c46f66a1b384ae38ffaa4402ee0919138d86f9a","source":{"kind":"arxiv","id":"1210.0405","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.0405","created_at":"2026-05-18T03:44:22Z"},{"alias_kind":"arxiv_version","alias_value":"1210.0405v1","created_at":"2026-05-18T03:44:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.0405","created_at":"2026-05-18T03:44:22Z"},{"alias_kind":"pith_short_12","alias_value":"KHLIMLKXAP5C","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KHLIMLKXAP5CHHR4","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KHLIMLKX","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:KHLIMLKXAP5CHHR4H5GBYRXWNI","target":"record","payload":{"canonical_record":{"source":{"id":"1210.0405","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-01T13:57:34Z","cross_cats_sorted":[],"title_canon_sha256":"52dd7d389235edc4228b2c9cdb658870c79def85fe4ae8b815d4b2a59e95f673","abstract_canon_sha256":"2ee4dc588b6ab4db321d55fd3b02a1d53e215f5f2dc241a8b6f6e545f2040368"},"schema_version":"1.0"},"canonical_sha256":"51d6862d5703fa239e3c3f4c1c46f66a1b384ae38ffaa4402ee0919138d86f9a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:22.526829Z","signature_b64":"iIYyYBkvOWW4FKk9XGheditNeO4Z0bd0VofZdG6NcRSPHhjpoZoutd4/dEzggzwvFm2G8xu8PqSNAaEEPuXVCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51d6862d5703fa239e3c3f4c1c46f66a1b384ae38ffaa4402ee0919138d86f9a","last_reissued_at":"2026-05-18T03:44:22.526296Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:22.526296Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.0405","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":"2026-05-18T03:44:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iULZ1aX4p8E2uCpYPXSJUQaIIjjHXOAwEWy1GvC3unFX4hiiEqu+SOmyvLT+UyyjnZlHihN//Bx8rba5qtuEAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T16:43:51.646744Z"},"content_sha256":"024feea8ff0a1f98079e2ab781af5866938cfb64cfe0824f98207cae754c7cf9","schema_version":"1.0","event_id":"sha256:024feea8ff0a1f98079e2ab781af5866938cfb64cfe0824f98207cae754c7cf9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:KHLIMLKXAP5CHHR4H5GBYRXWNI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Isoperimetric Sequences for Infinite Complete Binary Trees, Meta-Fibonacci Sequences and Signed Almost Binary Partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Anita Das, Frank Ruskey, L. Sunil Chandran","submitted_at":"2012-10-01T13:57:34Z","abstract_excerpt":"In this paper we demonstrate connections between three seemingly unrelated concepts.\n  (1) The discrete isoperimetric problem in the infinite binary tree with all the leaves at the same level, $ {\\mathcal T}_{\\infty}$:\n  The $n$-th edge isoperimetric number $\\delta(n)$ is defined to be $\\min_{|S|=n, S \\subset V({\\mathcal T}_{\\infty})} |(S,\\bar{S})|$,\nwhere $(S,\\bar{S})$ is the set of edges in the cut defined by $S$.\n  (2) Signed almost binary partitions: This is the special case of the coin-changing problem where the coins are drawn from the set\n  ${\\pm (2^d - 1): $d$ is a positive integer}$. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.0405","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":"2026-05-18T03:44:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xa0DIqWy4510VIT7EEenYVxLUs/7VLgzAylDvkPBIvKjt2Xm0BluWuakO9yR6lP11BiHFGOx487Q6fDD55kZCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T16:43:51.647448Z"},"content_sha256":"defb4e57eb9945c6351407e1040ef053519aa6a2959dafaf3e7db9aec274a2bd","schema_version":"1.0","event_id":"sha256:defb4e57eb9945c6351407e1040ef053519aa6a2959dafaf3e7db9aec274a2bd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KHLIMLKXAP5CHHR4H5GBYRXWNI/bundle.json","state_url":"https://pith.science/pith/KHLIMLKXAP5CHHR4H5GBYRXWNI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KHLIMLKXAP5CHHR4H5GBYRXWNI/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":"2026-05-28T16:43:51Z","links":{"resolver":"https://pith.science/pith/KHLIMLKXAP5CHHR4H5GBYRXWNI","bundle":"https://pith.science/pith/KHLIMLKXAP5CHHR4H5GBYRXWNI/bundle.json","state":"https://pith.science/pith/KHLIMLKXAP5CHHR4H5GBYRXWNI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KHLIMLKXAP5CHHR4H5GBYRXWNI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:KHLIMLKXAP5CHHR4H5GBYRXWNI","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":"2ee4dc588b6ab4db321d55fd3b02a1d53e215f5f2dc241a8b6f6e545f2040368","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-01T13:57:34Z","title_canon_sha256":"52dd7d389235edc4228b2c9cdb658870c79def85fe4ae8b815d4b2a59e95f673"},"schema_version":"1.0","source":{"id":"1210.0405","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.0405","created_at":"2026-05-18T03:44:22Z"},{"alias_kind":"arxiv_version","alias_value":"1210.0405v1","created_at":"2026-05-18T03:44:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.0405","created_at":"2026-05-18T03:44:22Z"},{"alias_kind":"pith_short_12","alias_value":"KHLIMLKXAP5C","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KHLIMLKXAP5CHHR4","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KHLIMLKX","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:defb4e57eb9945c6351407e1040ef053519aa6a2959dafaf3e7db9aec274a2bd","target":"graph","created_at":"2026-05-18T03:44:22Z","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 this paper we demonstrate connections between three seemingly unrelated concepts.\n  (1) The discrete isoperimetric problem in the infinite binary tree with all the leaves at the same level, $ {\\mathcal T}_{\\infty}$:\n  The $n$-th edge isoperimetric number $\\delta(n)$ is defined to be $\\min_{|S|=n, S \\subset V({\\mathcal T}_{\\infty})} |(S,\\bar{S})|$,\nwhere $(S,\\bar{S})$ is the set of edges in the cut defined by $S$.\n  (2) Signed almost binary partitions: This is the special case of the coin-changing problem where the coins are drawn from the set\n  ${\\pm (2^d - 1): $d$ is a positive integer}$. ","authors_text":"Anita Das, Frank Ruskey, L. Sunil Chandran","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-01T13:57:34Z","title":"Isoperimetric Sequences for Infinite Complete Binary Trees, Meta-Fibonacci Sequences and Signed Almost Binary Partitions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.0405","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":"sha256:024feea8ff0a1f98079e2ab781af5866938cfb64cfe0824f98207cae754c7cf9","target":"record","created_at":"2026-05-18T03:44:22Z","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":"2ee4dc588b6ab4db321d55fd3b02a1d53e215f5f2dc241a8b6f6e545f2040368","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-01T13:57:34Z","title_canon_sha256":"52dd7d389235edc4228b2c9cdb658870c79def85fe4ae8b815d4b2a59e95f673"},"schema_version":"1.0","source":{"id":"1210.0405","kind":"arxiv","version":1}},"canonical_sha256":"51d6862d5703fa239e3c3f4c1c46f66a1b384ae38ffaa4402ee0919138d86f9a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"51d6862d5703fa239e3c3f4c1c46f66a1b384ae38ffaa4402ee0919138d86f9a","first_computed_at":"2026-05-18T03:44:22.526296Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:44:22.526296Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iIYyYBkvOWW4FKk9XGheditNeO4Z0bd0VofZdG6NcRSPHhjpoZoutd4/dEzggzwvFm2G8xu8PqSNAaEEPuXVCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:44:22.526829Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.0405","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:024feea8ff0a1f98079e2ab781af5866938cfb64cfe0824f98207cae754c7cf9","sha256:defb4e57eb9945c6351407e1040ef053519aa6a2959dafaf3e7db9aec274a2bd"],"state_sha256":"108bdfe02fa902e94ad4c51b73802164eb3a27e3912a88f521f639ce7112e436"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tWw49xyr29vXRTfC090SLLEk5CsbhW+0DatQgEzPV1e1FV2ojBwy8cwNNNWAMuT72hLO8ui63Ehl9QW3QgKLBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T16:43:51.651082Z","bundle_sha256":"4144b8a9b6d0a8f82cd75acad4d4e4dbadb715e9f42a87c345a80a38727664ea"}}