{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ELTIK6URFMTC7WZXLVOQN7KT63","short_pith_number":"pith:ELTIK6UR","canonical_record":{"source":{"id":"1506.07497","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2015-06-24T18:53:06Z","cross_cats_sorted":["physics.soc-ph"],"title_canon_sha256":"2ccbb99bdba9a662eacabd6afaae439574afa41ab631f6d262b3693ce75deedf","abstract_canon_sha256":"a74a610f675da0b65519c4c7cb0569ef3dd95adc55248b1d30f801391a5eb5f2"},"schema_version":"1.0"},"canonical_sha256":"22e6857a912b262fdb375d5d06fd53f6d53e9476e6f9a894308cb64532305dbd","source":{"kind":"arxiv","id":"1506.07497","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.07497","created_at":"2026-05-18T01:39:53Z"},{"alias_kind":"arxiv_version","alias_value":"1506.07497v1","created_at":"2026-05-18T01:39:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.07497","created_at":"2026-05-18T01:39:53Z"},{"alias_kind":"pith_short_12","alias_value":"ELTIK6URFMTC","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"ELTIK6URFMTC7WZX","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"ELTIK6UR","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ELTIK6URFMTC7WZXLVOQN7KT63","target":"record","payload":{"canonical_record":{"source":{"id":"1506.07497","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2015-06-24T18:53:06Z","cross_cats_sorted":["physics.soc-ph"],"title_canon_sha256":"2ccbb99bdba9a662eacabd6afaae439574afa41ab631f6d262b3693ce75deedf","abstract_canon_sha256":"a74a610f675da0b65519c4c7cb0569ef3dd95adc55248b1d30f801391a5eb5f2"},"schema_version":"1.0"},"canonical_sha256":"22e6857a912b262fdb375d5d06fd53f6d53e9476e6f9a894308cb64532305dbd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:39:53.904117Z","signature_b64":"4ZvmTDgIkAxUB9nKlx/t6eT/D29xjeQQd6uLdMocIeEV3FrivMhJvLOpZ8rT4TG4LL2I8J30LEwbH815chrnCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22e6857a912b262fdb375d5d06fd53f6d53e9476e6f9a894308cb64532305dbd","last_reissued_at":"2026-05-18T01:39:53.903533Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:39:53.903533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.07497","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":"2026-05-18T01:39:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oFpsgr0U8HKI/N47y42fyBpItqE1ESz0TkQcx7js1J+Al6UDd68tVz8QC57FfyJvrKtwEPJfE01hmOtSRaZmAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T04:18:17.705845Z"},"content_sha256":"a6a9c25c1489491e697a6ea37d6c77781eb6f65721ee38b17589eb40ddfa4712","schema_version":"1.0","event_id":"sha256:a6a9c25c1489491e697a6ea37d6c77781eb6f65721ee38b17589eb40ddfa4712"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ELTIK6URFMTC7WZXLVOQN7KT63","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Two Power Series Models of Self-Similarity in Social Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.soc-ph"],"primary_cat":"cs.SI","authors_text":"Subhash Kak","submitted_at":"2015-06-24T18:53:06Z","abstract_excerpt":"Two power series models are proposed to represent self-similarity and they are compared to the Zipf and Benford distributions. Since evolution of a social network is associated with replicating self-similarity at many levels, the nature of interconnections can serve as a measure of the optimality of its organization. In contrast with the Zipf distribution where the middle term is the harmonic mean of the adjoining terms, our distribution considers the middle term to be the geometric mean. In one of the power series models, the scaling factor at one level is shown to be the golden ratio. A mode"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07497","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":"2026-05-18T01:39:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JQXuoUB6bHqzFlZC8uvvKhzgxWKINZJl3IHcCYzV/+9EPG/By6tkL2UswOFPqvt2Co8VwOdhcFLQdum2+/qKCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T04:18:17.706190Z"},"content_sha256":"93192f1c66397cd34c5122fbabbb49667923b035717a1f01760050f0657350b0","schema_version":"1.0","event_id":"sha256:93192f1c66397cd34c5122fbabbb49667923b035717a1f01760050f0657350b0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ELTIK6URFMTC7WZXLVOQN7KT63/bundle.json","state_url":"https://pith.science/pith/ELTIK6URFMTC7WZXLVOQN7KT63/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ELTIK6URFMTC7WZXLVOQN7KT63/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":"2026-06-01T04:18:17Z","links":{"resolver":"https://pith.science/pith/ELTIK6URFMTC7WZXLVOQN7KT63","bundle":"https://pith.science/pith/ELTIK6URFMTC7WZXLVOQN7KT63/bundle.json","state":"https://pith.science/pith/ELTIK6URFMTC7WZXLVOQN7KT63/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ELTIK6URFMTC7WZXLVOQN7KT63/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ELTIK6URFMTC7WZXLVOQN7KT63","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":"a74a610f675da0b65519c4c7cb0569ef3dd95adc55248b1d30f801391a5eb5f2","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2015-06-24T18:53:06Z","title_canon_sha256":"2ccbb99bdba9a662eacabd6afaae439574afa41ab631f6d262b3693ce75deedf"},"schema_version":"1.0","source":{"id":"1506.07497","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.07497","created_at":"2026-05-18T01:39:53Z"},{"alias_kind":"arxiv_version","alias_value":"1506.07497v1","created_at":"2026-05-18T01:39:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.07497","created_at":"2026-05-18T01:39:53Z"},{"alias_kind":"pith_short_12","alias_value":"ELTIK6URFMTC","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"ELTIK6URFMTC7WZX","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"ELTIK6UR","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:93192f1c66397cd34c5122fbabbb49667923b035717a1f01760050f0657350b0","target":"graph","created_at":"2026-05-18T01:39:53Z","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":"Two power series models are proposed to represent self-similarity and they are compared to the Zipf and Benford distributions. Since evolution of a social network is associated with replicating self-similarity at many levels, the nature of interconnections can serve as a measure of the optimality of its organization. In contrast with the Zipf distribution where the middle term is the harmonic mean of the adjoining terms, our distribution considers the middle term to be the geometric mean. In one of the power series models, the scaling factor at one level is shown to be the golden ratio. A mode","authors_text":"Subhash Kak","cross_cats":["physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2015-06-24T18:53:06Z","title":"Two Power Series Models of Self-Similarity in Social Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07497","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:a6a9c25c1489491e697a6ea37d6c77781eb6f65721ee38b17589eb40ddfa4712","target":"record","created_at":"2026-05-18T01:39:53Z","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":"a74a610f675da0b65519c4c7cb0569ef3dd95adc55248b1d30f801391a5eb5f2","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2015-06-24T18:53:06Z","title_canon_sha256":"2ccbb99bdba9a662eacabd6afaae439574afa41ab631f6d262b3693ce75deedf"},"schema_version":"1.0","source":{"id":"1506.07497","kind":"arxiv","version":1}},"canonical_sha256":"22e6857a912b262fdb375d5d06fd53f6d53e9476e6f9a894308cb64532305dbd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22e6857a912b262fdb375d5d06fd53f6d53e9476e6f9a894308cb64532305dbd","first_computed_at":"2026-05-18T01:39:53.903533Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:39:53.903533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4ZvmTDgIkAxUB9nKlx/t6eT/D29xjeQQd6uLdMocIeEV3FrivMhJvLOpZ8rT4TG4LL2I8J30LEwbH815chrnCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:39:53.904117Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.07497","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a6a9c25c1489491e697a6ea37d6c77781eb6f65721ee38b17589eb40ddfa4712","sha256:93192f1c66397cd34c5122fbabbb49667923b035717a1f01760050f0657350b0"],"state_sha256":"5aff1b821b31fbc297801e0b837cac18cc8d0f03964d9b4bbe7befcec1ee558f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"npANnxYSJhpZXNoUgxOJtEW2hKqTyHfsAqWn129dHaCWPPhDMy6mQkDAxAG15TZIcDDP8Lcoev/t04th7RCLAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T04:18:17.708157Z","bundle_sha256":"46e18919017698e5bd7215676cdb1f58f83809b0c32162f727a616e604ca4c07"}}